Soundcolor, are you sure of your info? The .223 and 5.56 are the same round. A 22 Magnum shouldn't chamber in a .22 LR (and wouldn't be a good idea to fire either)
The .223 and the 5.56 are not the same round. The 5.56 has a bigger casing, longer projectile, and more grains of powder. You can fire the .223 from a 5.56, tho you may have problems with the blowback being enough to cycle the next round into the chamber.
The extra powder in the 5.56 creates increased pressure in the chamber and barrel, and may cause chamber, or barrel failure. In addition, the 5.56 casing is slightly larger in circumfence, and thus seals extremely tightly in the camber, it may well fit inside the chamber tightly, but once fired, the casing will expand, and another round cannot be loaded into the chamber. If somehow the casing were to manage to be ejected, there is a strong possiblity that the projectile itself, (being both longer, and bigger in circumfrence) will lodge into the chamber, and upon the next round being cycled into the chamber and fired.... BOOOOOOOOM. you know what happens.
As for the .22, I may have mis-stated on the magnum. Your absolutely correct. What I meant to say is that a gun chambered for the .22magnum can fire a standard .22, and a gun chambered for the .22lr can fire a standard .22. But a gun chambered for a standard .22 cannot fire a .22lr, as the casing, and projectile are longer, and it cannot firea .22mag. Likewise, a gun chambered for a .22lr cannot fire a .22mag either.
jeez, i hope i wrote it right this time. So freakin confusing...