Ammunition comes in different lengths, shapes, and diameters depending on the type of bullet or case used. If the case is really small, chances are it is a .22 rimfire cartridge.
Years ago a wide variety of rimfire cartridges were available. Today, only .22 rimfire cartridges are commercially available. They can come in 22 short, long, long rifle, and magnum lengths. You will have to learn how to identify them by reading the information on the ammunition box as the data stamp is not on the base of the cartridge.
22 Hornet and 222 Remington use a .22 caliber bullet but use a centerfire cartridge case.
A rimfire cartridge will travel 1300 feet per second while a centerfire cartridge will do over 2000 feet per second. The centerfire case is bigger than the rimfire case and holds more powder.