Sure, the terms “rimfire” and “centrefire” refer to how a cartridge is constructed. In the case of centrefire ammunition, the primer is located in the centre of the cartridge base, hence centrefire, and the primer consists of a small capsule of shock-sensitive explosive that is ignited when struck by the firearm pin of the firearm. There's a small hole between the pocket that the primer sits in that connects it with the interior of the cartridge, which contains the propellant powder. When the cartridge is fired, the firing pin strikes the primer, and the blow to the primer causes the propellant inside that to ignite, which produces a flame that goes through the small hole—that's called a flash hole—connected to the interior of the cartridge case, which ignites the main powder charge, which then propels the bullet down the bore.
In contrast, rimfire cartridges are manufactured with the shock-sensitive priming composition located around the rim of the cartridge. When the cartridge is fired, the firing pin crushes the priming composition between the two sides of the rim, which causes ignition. After that, it works the same as for centrefire.