As the folks have said, .22 Mag and .22 LR are two different birds.
HOWEVER- there IS another round the .22 Mag CAN fire safely and accurately- that is the .22 WRF- or .22 Winchester Rimfire. Older (and shorter) than the mag, lead bullet instead of jacketed, does not do as much damage to squirrels and bunnies. Rimfires headspace off the rim, so as long as you clean chamber good after shooting, does not matter.
BTW, there are a few revolvers that will shoot LR or magnum. (I have a Colt Peacemaker like that) They have two different cylinders, barrel bored for Mag, meaning accuracy with LR is wishful thinking.