A brief history is that the HK G3 came from the CETME design and is currently or has been used by almost every military in the world and is a popular choice for terrorist organizations. I'm not going to discuss every variant, only the popular ones (if you care to learn about the individual variants I will be glad to detail them to you in a PM).
G3: This is the very first G3, it was based off of the CETME Modelo B. It was a select-fire assault fire that used the 7.62x51mm NATO round (also known as .308 Winchester). At this time I am not aware of any airsoft copies of the original version of the G3.
G3A2: This is first version to feature the drum sights.
G3A3: This is the version that sported the plastic stock, handguard, and pistolgrip.
G3SG/1: This version is the known designated marksman variant. These variants received a new trigger group, a cheek rest, and a slightly extended stock. The TM G3 SG-1 is a copy of this variant.
G3A4: This is the same as the G3A3, but it sports a collapsible stock. The CA M41 ES is a copy of this variant.
G3KA4: The version that features the same retractable stock in conjunction with a 315mm barrel. The K stands for Kurz with means short in German and is a common designation for German companies to use on shortened rifles and SMGs.
G3A4ZF: A G3 with a scope bracket and scope.
HK21: This is the machinegun version, capable of being fed by both belt and magazines. It is common on the American aftermarket os Pre-86 automatics to modify these weapons to accept .223 and .308 sears (the HK23 was the 5.56mm version). One of the unique features is this gun's high firing rate (800rpm or 900rpm depending on HK21 model and 750rpm for the HK23). I wish they would make an airsoft version of this beast, as its firing rate would easily place it amongst the most feared SAWs.
HK11: Experimental rifle that attempted to use 4.7mm caseless ammunition. The reason for its cancellation are under speculation, but a good guess is the economic strain of uniting East and West Germany.
HK51: This was an experimental model but was dropped. Modern reference to an HK51 actually means a modified G3 that uses sear parts to allow it to fire several calibers. The term is often misunderstood to mean a G3 that has been reduced to the length of an MP5. The MC51 was a version created by FR Ordnance for the British SAS, but it was not made by HK.
HK53: This is the version which many people get in their mind when they think of an HK51. It sports a 211mm barrel and retractable stock that it give it characteristics much like the MP5. What seperates this gun is that it fires the 5.56mm round instead of the G3's standard 7.62x51mm round.
G3A1: There was an earlier version of this rifle, but now it is commonly used to refer to a G3 on the American market that is equipped with an aftermarket stock.
HK41: This is the rarer of the civillian versions shipped to America. It was limited to semi-automatic fire only, but could easily be modified to fire in full-automatic mode because it used a modular trigger system common to all G3s.
HK91: This version fixed the modularity issues allowing for full-auto HK41s to be created. Many experts consider it to be clumsier and not as high of quality as the HK41 and is not as desirable on the American market.
PSG-1: One of the most revered police sniper rifles in the world. It received a highly modified barrel to be used for long range accuracy (notably it also features polygonal rifling). The trigger group was modified to only fire in sem-automatic form. The iron sights were removed and a scope was mounted. It contains many adjustable features commonly found on modern sniper rifles. This gun, even though it is so famed for its accuracy and reliability, is rarely seen because it carries a $10K+ price tag.
MSG-90: The shorter, lighter, cheaper military variant of the PSG-1. Currently used by the US in the DMR program.
MSG-3: The major difference is that this is an SG1 that uses the newer type of scope mount.
Other Airsoft Variants
TM MC51: Presumably a copy of the FR Ordnance MC51 version that was manufactured for the British SAS but was quickly dropped.
TM G3 SAS: This is not actually a real gun, but the closest relative is a G3 pistol known as the Vector V51. The Vector is a version that was manufactured to be a civillian-legal short G3, meaning that in order for it to not receive an NFA SBR title it could not have any kind of stock (retractible or fixed) and thus the G3 pistol was born.
Classic Army: All Classic Army M41 and SAR variants are not copies of any HK, but rather of Schwaben, a German company licensed to make reproductions of the G3. The CA53 could be a copy of the HK53, but more information is needed at this point as to whether this is a copy of HK or Schwaben.
If there is anything that you feel should be added just let me know.