Final answer:
The correct answer is 'rimfire cartridge,' which differs from shotshells and centerfire cartridges by having the primer located in the base's rim.
Step-by-step explanation:
The type of cartridge that is different from the shotshell and centerfire cartridge is the rimfire cartridge.
Rimfire cartridges are a type of firearm cartridge in which the firing pin strikes and crushes the base's rim to ignite the primer. This is in contrast to centerfire cartridges, where the primer is located in the center of the cartridge case head. Unlike shotshells, which are typically used in shotguns to fire a number of small pellet-like projectiles, rimfire cartridges are mostly used for small caliber pistols and rifles. The most common example of a rimfire cartridge is the .22 caliber.