Ok I'll take a crack at this from a user's practical point of view. Not a historian or gunsmith, so I'm not going to try to get into all the hairy details and embarrass myself. Even though the term sporting/non-sporting rifle may be used to explain some models, I thorougly reject its validity.
SKS: 7.62x39 Semiauto rifle, Usually have that little nub of a mag, but some can accept full size ak banana mags.
AK47: 7.62x39 Full auto assault rifle (we get semi auto versions)
AK74: 5.45x39 Full auto assault rifle (we get semi auto versions) with some internal changes
SAR: Romanian AK imported by Century. Some parts are romanian, other parts are US to comply with the thing about non sporting rifles having X number of US parts are ok to import. Generally anything that comes out of Century like this (SAR, WASR, FALs, etc) looks like a bunch of monkeys did it. All this monkey stuff is fixable pretty easily if you take a look at the linx310 site for more explanation, or you know what to look out for when you go shopping and avoid the guns with the problems. SAR-1 is 7.62, SAR-2 is 5.45, and SAR-3 is .223. SAR-3 was designed around a metal east german Weiger mag, so if you hear about feeding problems, it's usually somebody using a mag other than the weiger mags with them. No problems here with my SAR-3 except the day I ran out of Wolf ammo and decided to use up the box of "Hey, try a box of this" polymer cased .223. As the second round got picked up to be fed the plastic MELTED and blew up in my face. I don't think the gun got hurt, as the gas left via the half open side of the receiver instead of having to find the metal with the most give. Should've seen to look on the newbie shooter's face who was watching!
WASR: One day the ATF said "No More SARs" to Century. Apparently it was still a no-no for the gun to have high cap mags even though it went through all the hoops with the parts monkeys. The solution to this was to make a gun that could only accept single stack low-cap mags. And so now WASRs come out of Century instead of SARs (built by the same monkeys, except a little older and a little blinder). The strange thing is, I've never seen a low cap WASR, though I know they exist. By the time they get to Four Seasons or an owner's hands, somebody takes a dremel or something to them and makes them into a gun that can accept double stacks. There's definitely a WASR-1 and WASR-2 in the same caliber scheme as the SARs. I read somewhere there's a WASR-3 but I've never seen or heard of someone who actually owns one.
RPK: "Machine gun" version of an AK with 50% thicker receiver metal and other beefyness.
VEPR: Semiauto AK made for civilians based off a beefy RPK receiver. 5.45, 7.62, .308, and .223. Imported by Robinson Arms. Good quality, not like Century.
Saiga: Semiauto AK made for civilians that the russian company goes way out of their way to make into a "sporting" rifle that can't be unmade into a non sporting rifle easily. Most prominent change is the placement of the trigger guard and fire control group way in the back of the receiver so that you can't put an AK pistol grip on it (or any other stock designed for AKs). It's possible with tools to move that FCG forward Comes in 7.62, .308, .223, and 12 gauge(!). If the 12 gauges ever get cheap again, I'm getting one.