What are the natural and artificial sugars?
Sugar, as in common table sugar from sugar cane, is sucrose, which is a chemically weak linked combination of glucose and fructose. Your stomach acids will split sucrose very fast. So the difference in using natural cane sugar and factory split glucose may only be a matter of minutes once you eat the stuff

Same goes for almost all the sugars other than the "artificial sweeteners" which are generally not sugars at all, they just taste very sweet

Some artificial sweeteners are very natural in the general scheme of things when compared to processed sugar etc.

Nearly everything that comes in a packet with a barcode is not "natural". White table sugar is not natural. Buy some sugar cane stem, and crush and boil it, then you can see the difference

I would rather use the white table sugar though, as it is more likely to be clean and tested as being non-contaminated

Sugar Substitutes

There is a great list of sugar substitutes including artificial sweeteners on Wikipedia. Many of which would be better for you if sugar levels was of a concern in your diet (it is for some people). Many are useless in baking

The list of "artificial sweeteners" is thus:


Acesulfame Potassium (Celanese, Nutrinova, Sunett)
Advantame
Alitame
Aspartame (Equal, Neotame, NutraSweet)
Aspartame-Acesulfame Salt (Twinsweet)
Dulcin
Glucin
Neohesperidin Dihydrochalcone
P-4000
Saccharin (Sweet'N Low)
Sodium Cyclamate
Sucralose (Splenda)


And the sugar alcohol's, which are also a form of "artificial sweeteners"


Erythritol
Glycerol
Hydrogenated starch hydrolysates (HSH) (long sub list) 
Isomalt
Lactitol
Maltitol
Mannitol
Sorbitol
Xylitol


Nice info-graphic from Washington Post