CO2 requires the small gas bottles. Multiple shots, but when the bottle is empty, you are done unless you have another one.
Air rifles are either break action, with one pump moving a large piston that is spring powered to produce pressure, or they are pump guns that fill a chamber with more pressure for every pump. Unlimited shooting, nothing but elbow grease required.
The break actions also sometimes use nitrogen filled cylinders.
There is also a family of air rifle guns that uses an out board source of pressure, either an air tank or a pump, to fill the reservoir on the gun, allowing multiple shots per refill. Depending on what you are doing, some people feel the need to carry the tank or pump along.