This is a nice overview of common types but I still don't understand the "why" of some of their names, such as the difference between a .38 and a .380 (It's the same number!)
If you think having 2 cartridges that both have .38" caliber bullets is confusing, take a look at all the 9mm ones. Just in the ones that are actually called 9mm and not just caliber equivalent, there's 9x19, 9x25 mauser, 9x57 mauser, 9x39, 9mm winmag, 9x18 makarov, and a ton more I can't remember. Some of those are rifle cartridges, some handgun. They have different bullets with different characteristics and different bullet lengths and different bullet weights. And the shape of the cartridges behind them, the guns they fire from, and the amount of propellant each one has is all different.
ETA: and in the case of both these rounds, .38" is actually the approximate diameter of the _case_ not the bullet; the diameter of .380 ACP bullet is 9mm, and the diameter of .38 Special is .357".