As others have correctly pointed out in addition to being longer, a .22 mag is also just a touch....1 thou I think larger in diameter than .22 S, L, and LR.
Thus .22 will fit in a .22 mag cylinder, but is not the correct caliber. .22 mag will not fit in a .22 cylinder, thank goodness, .22 mag is much higher pressure.
.38 and .357 can interchange in a .357 revolver. They are the same diameter. Problems do crop up if a lot of .38 has been shot in a .357 cylinder. A good cleaning will put it right.