You're right about rim fire cartridges being used, almost exclusively, in small calliber firearms today. However, that wasn't always the case. In the early days of firearms, here in the U.S., almost all calibers were rim fire cartridges. There is really no difference except that in rim fires, the entire end of the cartridge is the
primer... a type of small explosive charge that fires when struck by the firing pin after one pulls the trigger. This over against the center fire cartridge which has the same type of primer but it is contained within a smaller area, as the name implies, in the center of the cartridge end. The advantage of the center fire is that the primer, once fired, can be pressed out of the cartridge which can then be reused by pressing in another primer. Additionally, there's an additonal, albeit small, safety factor in that the bullet can be fired only when the much smaller center fire primer is struck, rather than the entire end of a large caliber one... By the way, here's some pictures of old center and rim fire cartridges:
http://www.oldammo.com/november05.htm