What's the difference between drawing paper and regular paper?
TL;DR:  Generally speaking, printer paper is not designed to last long, and is intended to hold ink rather than graphite, charcoal, paint, etc.  The same is more or less true of notebook paper.  Printer and notebook paper have very little tooth (roughness); lack weight (i.e., the sheets are thin); and have relatively high acid content, which means they will yellow and become brittle over time.





Different Kinds of Drawing Paper:

The main differences:  Tooth and Weight

Weight:

"Weight" is basically (as the term implies) a measure of how thick and heavy each sheet of paper is.


  Thicker or heavier papers can handle more water or paint without buckling, curling or falling apart. Traditionally, papers are measured by the weight in pounds of one ream, approximately 500 sheets. If a paper comes in different sizes, its weight will vary even though the thickness has not changed. Each paper type uses a certain size as its "standard." A ream of standard 22" x 30" watercolor paper (500 sheets) would weigh 300 lbs. The very same thickness paper in a 40" x 60" sheet would have a weight of 1,114 lbs. for the ream of paper. Its weight changed due to the size of the sheets, not the paper's thickness, but the paper is still designated as 300-lb. 
  
  The inconsistency of this traditional method has led to the use of metric measurements or grams per square meter or gsm. When paper is measured in gsm, its weight will not change with the size of the sheet. The same 22" x 30" sheet of watercolor paper described above would weigh 640gsm, meaning that a square meter of this paper would weigh 640 grams. Larger size sheets of that same paper, like a 40" x 60" size sheet, also would weigh 640gsm. While different sizes, the square meter remains constant, as does the thickness of the paper.
  -  Dick Blick


And:


  Weights (relating to thickness) of paper are standardized and defined by the International Organization for Standardization and are often listed in grams per square meter (gsm), or in pounds, the standard of measurement more familiar to most artists in the U.S.  Following are some of the most common weights of paper found in sketchbooks and drawing pads (all measurements are approximate):
  
  25 lb (approx 40 gsm):  tracing paper
  30-35 lb (approx 45-50 gsm):  newsprint
  50-60 lb (approx 75-90 gsm):  sketching or practice paper — thick enough to work on with pencils, charcoal, or pastels, but usually too thin for ink or most markers, which may bleed through.
  70-80 lb (approx 100-130 gsm): drawing paper suitable for finished artwork in most media.  Paper any lighter than 70lb will usually be thin enough to see through to drawings or materials underneath.
  90-110 lb (approx 180-260 gsm):  heavy-weight drawing paper, bristol, multi-media papers.  Weight in this range is similar to card stock or light poster board.
  Heavier papers, up to 140 lb (approx 300 gsm) or more, are most often used for painting rather than drawing.  When found in sketchbooks, they are usually rougher papers intended as watercolor journals or to remove for painting on individual sheets.
  -  Muse Art and Design


And:


  Sketch paper is the thinnest, lightest paper, varying from 30 to 60 lbs. It isn't meant be used for finished drawings, as most will discolor and degrade quickly. However, it's economical, and perfect for short studies, thumbnails, compositional sketches, and working out ideas.
  
  Watercolor or printmaking paper has to be the thickest, heaviest paper because it must withstand the moisture from the water media applied to it. It usually weighs between 90 and 140 lbs. (The smoother, hot press watercolor papers can be great for drawing, also!)
  
  Graphite or charcoal drawing paper doesn't need the durability of watercolor or printmaking paper, but is heavier than sketch paper. It usually weighs between 70 and 100 lbs. The weight you choose should depend on how you work with your medium.
  -  Drawing Source




Tooth:

"Tooth" is a measure of how rough or smooth the paper's surface texture is.  The more tooth a paper has, the rougher it is, and the better it will take soft art media like charcoal and pastels.  The less tooth it has, the smoother it is, and the better it will be for fine detail work, harder graphite, pen and ink, etc.  Wet media (ink, watercolors, etc) will be more likely to bleed on a toothier paper;  dry media (charcoal, pastels, etc) will be more likely to slough off of a paper with less tooth.


  Surfaces are described as having more or less “tooth,” or roughness in texture. The more toothy the paper, the rougher its surface. 
  
  Rougher surfaces are generally found more in thicker papers. Thick, toothy surfaces hold on to more of the drawing or painting medium and are better for high contrast and lower detail works. Toothier papers are well suited to charcoal, crayon and pastels, ink washes and watercolor, or any work that utilizes the texture of the paper for aesthetic effect. 
  
  Smoother surfaces take up less media and are better suited to more detailed work. Very lightweight papers like tissue paper, and lightweight sketch paper are usually smooth, but thicker papers like bristol and some painting paper are also smooth. Smoother surfaces are ideal for graphite pencil, colored pencil, and ink pens. Smoother papers are also more likely to be bleedproof, meaning that ink or color washes won’t spread and “feather” across the surface.
  -  Muse Art and Design


And:


  Rough paper is chosen for its definite texture. It is the natural result when a sheet is allowed to air dry without smoothing or pressing. Rough surface paper is a good choice for transparent watercolors used in a bold and immediate style, as it allows the pigment of color washes to settle into the hollows of the paper. Pastel artists also generally prefer a paper with "tooth" or texture to grab onto the pastel pigment.
  
  Cold Press paper, which is the most popular and versatile, has a slight texture. Handmade papers achieve this by re-pressing a new wet sheet, which smoothes the surface to some degree. Machine-made papers get a similar effect by placing the wet sheets between cold metal rollers. 
  
  Not/Cold Press: A "Not" sheet means it is "not hot press," and the term is often used instead of cold press.
  
  Hot Press paper is very smooth. It is made by running a freshly formed sheet through heated metal rollers or plates. Much like a clothes iron, this smoothes out any texture left by the earlier stages and creates a flat, hard, featureless surface. A good choice for highly detailed illustrations, it is also used for printmaking, etching, drafting, sketching and drawing.
  -  Dick Blick




Secondary coniderations:  Fiber and Sizing

Fiber (and acidity):


  Paper is made from a variety of plant sources. Whether the fibers come from cotton or other plants such as linen, flax, jute, hemp, bamboo, rice straw or rattan, they all provide cellulose fibers or plant cells of varying dimensions. A sheet of paper is basically a thin layer of mingled cellulose fibers. Most commonly, three types of fibers are used to produce papers for drawing and painting: cotton, cellulose and a combination of fibers. 
  
  Cotton papers, made from the longest cotton fibers, are generally considered the highest quality. They are referred to as being 100% cotton rag and can handle heavy erasing and working without tearing or showing wear. High-quality 100% cotton paper can last more than 100 years. However, not all cotton papers are the same. Those made from the lesser-quality, shorter cotton fibers can get fuzzy with reworking. 
  
  Cellulose papers are usually made of wood pulp and naturally have an acid content that will destroy the paper over time. The more acidic a paper is, the shorter its life expectancy. Buffers can be added to make the paper neutral.
  -  Dick Blick


And:


  Many papers are acid free. This designation means that the paper has a neutral pH (around 7). Acid-free papers should be selected for work intended to last for long periods of time because papers with higher acid content will deteriorate much faster. For most cellulose-based papers, acid-free also means that lignin and sulfur have been removed from the paper. These are the ingredients in wood-based papers that fade ink and turn paper yellow over time.
  
  Cotton and cotton-rag paper do not contain cellulose and are naturally acid-free. Cotton-based papers are also stronger, often thicker, hold up better to a lot of erasing, and perform well for wet media such as watercolor or ink washes. Cotton is often blended with cellulose to add strength and durability to paper. Premium archival papers will often list a ratio of cotton and wood fiber.
  -  Muse Art and Design 


And:


  pH neutral means that the paper had a neutral pH (7) at the time that it was made, but may still contain ingredients that can become acidic over time (for example, the size used to seal the paper).
  
  Acid free means that nothing acidic (and nothing that can become acidic) was introduced to the paper at any point in the paper-making process. 
  
  Some manufacturers (such as Strathmore) take further precautions and make paper at a slightly basic pH of 7.2 to 7.5.  This provides an alkaline buffer to help counter anything acidic that it may come into contact with.
  -  Drawing Source


And:  


  The rate and severity of deterioration result from internal and external factors: most importantly, the composition of the paper and the conditions under which the paper is stored.
  
  Paper is made of cellulose -- a repeating chain of glucose molecules -- derived from plant cell walls. One measure of paper quality is how long the cellulose chains, and subsequently the paper fibers, are: long-fibered paper is stronger and more flexible and durable than short-fibered paper.
  
  In the presence of moisture, acids from the environment (e.g., air pollution, poor-quality enclosures), or from within the paper (e.g., from the raw materials, manufacturing process, deterioration products), repeatedly cut the glucose chains into shorter lengths. This acid hydrolysis reaction produces more acids, feeding further, continued degradation.
  
  Mechanical pulping produces paper with the shortest fiber length and does not remove lignin from the wood, which promotes acid hydrolysis. Newspapers are printed on mechanically pulped paper. Chemical pulping removes lignin and does not cut up the cellulose chains as thoroughly as mechanical pulping, yielding a comparatively stronger paper, but which is still not as durable as rag paper.
  
  Wood pulp paper from before the 1980's also tends to be acidic from alum-rosin sizing (added to the paper to reduce absorbency and minimize bleeding of inks), which, in the presence of moisture, generates sulfuric acid.
  
  Acids also form in paper by the absorption of pollutants -- mainly sulfur and nitrogen oxides. Book leaves that are more brown and brittle along the edges than in the center clearly illustrate this absorption of pollutants from the air.
  
  Research by the Library of Congress has demonstrated that cellulose itself generates acids as it ages, including formic, acetic, lactic, and oxalic acids. Measurable quantities of these acids were observed to form under ambient conditions within weeks of the paper's manufacture. Moreover, paper does not readily release these acids due to strong inter-molecular bonding. This explains why pH neutral papers become increasingly acidic as they age.
  -  U.S. Library of Congress




Sizing/Absorbency:

"Sizing" is an additive that makes the paper more resistant to moisture.


  Papers intended for wet media (paints or inks) are made with sizing, a starch or gelatin that is either included in the paper pulp during the paper-making process, or is applied to the surface of the paper.  Sizing prevents liquid from absorbing too quickly into the paper, allowing some working time to lift, lighten, or move paints or inks by applying more water.  Sizing also helps protect the paper from getting too soggy, which can result in tearing and wrinkling.  Sizing can also help prevent finer ink or paint lines from spreading and feathering.  Sketchbooks intended for wet media should indicate on the cover that the paper is sized.
  -  Muse Art and Design


And:


  Sizing is added to make paper more water-resistant. It keeps the paper from absorbing too much moisture or pigment and helps to keep watercolors or inks brilliant. It also keeps lines and edges looking crisp. It is less important for papers used for dry media. Sizing also can factor into a paper's archival qualities - whether it will sustain or deteriorate over time. 
  
  Internal sizing is added while the paper pulp is still in a liquid state and is maintained in the matter of the paper. 
  
  External, Surface or Tub sizing is applied to the surface of the paper after the sheet is formed and dried. Some paper is both internally and surface-sized.
  -  Dick Blick




Other considerations:

Binding:

Sometimes a matter of mere personal preference, sometimes a matter of necessity, "binding" refers to how - and whether - the sheets of paper are connected to one another:


  Hard-bound sketchbooks have a hard cover and a sewn joint, just like a hard-bound book. These sketchbooks generally contain medium weight paper, about 70 lb. Hard-bound sketchbooks are the toughest and sometimes the expensive. They take more wear and tear, and generally survive longer than spiral or tape-bound books. Depending on the quality and method of binding, hard-bound sketchbooks often do not lay flat when opened all the way, so they can be difficult to use for larger drawings or for writing. Hard-bound sketchbooks are also less likely to have perforated pages, so they’re better thought of as real archival sketchbooks.
  
  Spiral-bound sketchbooks sometimes have hard covers but their covers often consist of a hard back cover and a thick paper front. Because of this construction, spiral-bound books are a little less hardy than hard-bound sketchbooks. Spiral-bound sketchbooks open flat when put on a surface, so they can be good for ink and paint washes. Spiral-bound sketchbooks often have perforated pages, so pages are easy to remove and have a clean edge for presentation, duplication, mounting, or framing
  
  Tape-bound sketchbooks generally have fewer pages than hard-bound and spiral-bound sketchbooks and do not have substantial covers. Tape-bound sketchbooks are not rugged, long lasting sketchbooks. Sketchbooks bound in this manner come in a wide variety of surface types and weights, ranging from very thin tissue and tracing paper to heavy bristol and vellum papers. Sometimes, tape-bound sketchbook pages are perforated, but often the pages are held in by a line of adhesive so it is not difficult to pull them out.
  -  Muse Art and Design


And:


  Single sheets are a great way to experiment with a limited quantity of paper. They will often require stretching and taping to remain flat if wet media is being used. 
  
  Blocks are a stack of paper glued or bound together on all four sides and mounted on a backing board. A block keeps the paper stretched as you paint. Once the painting is dry, the sheet is removed by inserting a knife between the sheets and gently breaking the binding. Blocks are a good choice for working wet, outdoors or while traveling. The disadvantage is that you can only use one sheet at a time.
  -  Dick Blick   






Printer Paper:

Compared to drawing paper, printer paper is cheaper, lower weight, more acidic, has less tooth, can't handle wet media, doesn't take much dry media, can't handle wet media, and is generally crappy in every important respect.  It works for doodling, but if you want to make something really beautiful and long-lived, you need quality paper.