The difference between the two is the diameter of the case. The .22LR's case is the same diameter as the bullet and the bullets have a rebated base to fit inside the case (pull a .22LR bullet and you'll see what I mean). The .22WMR's case is larger in diameter than the bullet and the bullet is not rebated, so it seats inside the case like a normal pistol cartridge and has a distinct mouth. Since the bullet diameters are the same (within a couple thousandths of an inch), this makes the WMR case larger in diameter than the LR case. This would allow the LR case to sit in the chamber canted to the bottom side because of the extra space, and also allow the very thin walls to blow out when they try to fireform to the larger WMR chamber resulting in gas leaks.
That is why it's not a good idea to load LR's in a WMR chamber. On a postive note, it is not possible to chamber a 22 WMR in a LR chamber at all. It simply won't fit.
.22 Long Rifle:
.22 Winchester Magnum Rimfire:
Note the differences in the cases, specifically at the mouths.
Mike