BB guns are powered by air. How they get that air is where things different. CO2-powered guns doesn’t use air per se, but they use compressed CO2 to project a BB down a barrel. CO2 guns are most commonly semi-auto or full-auto, and they utilize small 12-gram CO2 cartridges that plug into the gun.
These do require extra money due to the design of the cartridge.
Lever-action guns like the old school Red Rider utilize a pump activated by a lever. When cocked, the lever draws in air and loads the next round. The lever must be activated for every shot.
Pump guns feature an air pump often built in the front end. The shooter loads a round into the chamber and then pumps the gun to gather air to propel the round. The act of pumping the gun can be done once or over and over with some guns to gather more power behind the round.