What is the difference between centerfire and rimfire rifles?

Answer 1

A center-fire cartridge has a primer on the base or bottom, as the firing pin or hammer strikes the primer-cap it ignites the powder through a hole ( or two holes) inside the cartridge. A rim-fire has a flat metal rim on the base and no primer (such as a .22cal LR.)

Answer 2

Rimfire cartridges have the primer charge packed into the rim, and it is activated by a hammer hitting the rim and setting off the firing charge.

Centrefire cartridges have a separate primer which is inserted into the rear of the cartridge casing, and this is actuated by a firing pin making contact with the primer and setting off the primer charge.