NiCad and NiMH are very similar but each have their own pros and cons, i.e. NiCad is marginally better in cold weather, NiMH has a greater energy density, etc... read up at
http://www.batteryuniversity.com/partone-3.htm
One should also note that there has been a large amount of development of NiMH cells in recent years. High end NiMH cells (GP3700, IB3800) can push more current than the best NiCad.
There's a good bit of info about Lithium based batteries here:
http://www.batteryuniversity.com/partone-5.htm
Calvin, airsoft mini batteries are 2/3A cells, butterfly, ANPEQ (generally) and AUG batteries are A cells, and large batteries are SC.