What do 'woolen spun' and 'worsted spun' mean?
Woolen spun and worsted spun are references to the way the yarn is actually spun in the spinning process.  Worsted spun yarn includes individual fibers that are facing in many directions, whereas woolen spun has all of the fibers facing in the same direction before the yarn is spun and they remain much more parallel in the final spun singles. The process of spinning the two types of yarn is different as well, but less important to know if you are the end user of the yarn.

Woolen spun tends to incorporate more air between the individual fibers, so a woolen yarn will weigh less than a comparably thick yarn that is worsted spun.  The additional air also helps heat retention, so garments made from woolen spun yarn can be lighter weight and still warmer than those made from a comparably thick worsted yarn.

However, because the individual fibers don't overlap each other the way they do in a worsted yarn, woolen spun yarn doesn't hold up over time as well as a worsted spun yarn.  It is also more likely to pill.

As for when to use which one--well the opinions on that question are all over the place.  I suggest googling "woolen vs. worsted yarn" and you will read a hundred different opinions.  But, in general, I would avoid woolen spun yarns for projects that are going to get alot of rubbing, pulling, tons of wear.  Be cautious about using a woolen spun yarn for something you are going to put on a kid, for example.  But a shawl would be the perfect use for a woolen spun yarn, because you are looking for additional warmth with minimal weight when you make a shawl, AND it is less likely to be subject to the type of usage that will cause pilling.

One confusing element is that worsted in this context means the fashion in which the fibers are prepared (and spun), whereas worsted is also used in many parts of the world to indicate yarn of a specific thickness. These two definitions have absolutely nothing to do with each other--so you could spin a woolen yarn that is worsted weight, and confuse the heck out of everyone. You could also spin a non-wool fiber using the woolen spin technique (I think--better spinners than I feel free to disagree), and then have a cotton yarn, for example, that is woolen spun.  Super confusing.

Another important concept--singles vs. plied yarn.  When you first spin fiber into a strand of yarn, you have what is called a single.  The individual fibers are held together by adding twist into them--the amount of twist determines how strong the actual yarn is.  But think about what happens if a child sitting on a swing spins around a bunch of times and puts a twist in the ropes holding the swing.  They actually built up alot of energy in the ropes as they created that twist, and let go, the ropes release that energy by unspinning really quickly. 

Singles yarn is called "energized" because it has a similar inherent energy in it.  When you work with singles yarn, your final product will be much less consistent, even and smooth, because even after it is worked, the singles yarn is continually trying to release some of that built-up energy.

When you ply yarn, you take a number of singles (I think three plies is the most common), and twist them together in the opposite direction from the twist you used to combine the fibers into a single strand. The aim when creating a plied yarn is to balance the residual energy from the singles without actually untwisting the yarn and having the individual fibers fall apart. When you ply yarn, you are specifically trying to create yarn that is balanced--you should be able to drop a strand of plied yarn and it will not try to untwist in either direction.  Working with plied yarn tends to create smoother, more even and more regular final products.  

The last issue I will mention is the directionality or type of twist in your yarn. Yarn can have an S twist or a Z twist.  This describes the direction the yarn was plied (and is compared to the direction of the center element in these two letters). If you hold up a piece of yarn and look closely, you will see that the individual threads (or singles) spin in a direction that either looks like an S (they start at the top left of the strand and move diagonally to the bottom right) or a Z (they start at the top right and move diagonally to the bottom left).  The technique that you use for knitting or crocheting can interact differently with the different twists--some techniques might twist the yarn in such a way that it comes partially untwisted as it is worked.  Because twist is what gives yarn its final strength, this can actually have an impact on the strength of your final piece.

This is a pretty complex issue, and I don't know enough about it to be able to explain all of the permutations here.  My suggestion is to try and determine what type of technique you use for knitting (are you a thrower or a picker? Continental vs. English?) and/or crocheting (I don't know the equivalent terminology for crocheting, but I know that as a kid I used to crochet in a way that twisted the yarn less than I do know as an adult).  Once you know what to call your technique, you can start searching for that technique in combination with "S or Z twist" and see what people say about which works better in which situation.