I know absolutely nothing about air rifles. Do you need pellets for all air rifles, or can you use regular bullets? As in a .357cal, can you use .357cal projectiles like one does in a regular pistol?
Air rifle "caliber" denotes the size the barrel is drilled for, but as Fubarski said, the power level is less than a firearm of the same barrel size - so the projectile is necessarily lighter, velocity much less.