This is a clip:
It holds ammo to be loaded into a magazine.
This is a magazine:
It is what ammo is loaded into, and what the firearm uses chamber additional rounds. A magazine doesn't have to be detachable. An M1 Garand is a popular example of a rifle that uses clips to load it's integral magazine:
If the device on your .22 looked like the first image, it's a clip. If it actually holds the ammo, and is what the gun uses to chamber a round, it's a magazine.
Sorry for the lesson...it's a pet peeve of mine. It may just be semantics, but there is a complete functional difference between a clip and a magazine.