As far as .22 rimfires go, there are only two that share the case diameter and bullet dimensins: the older .22 Winchester Rim Fire (WRF) that is more than 100 years old, and the .22 Winchester Rimfire magnum (WRM) that was introduced in 1960. The older WRF had a lead bullet, and the newer WRF has a couple varieties of jacketed bullets.
The older WRF can be safely fired in standard WRM chambers. The reverse is not true.
The "22 Magnum" is the same as the .22 WRF cartridge.