The 5.56 round was designed after the common sporting round, but has two slight, although important, differences. Both are minor, but enough to cause some major if not deadly problems if you put 5.56 into a .223 chamber. .223 may be fired in a 5.56 chamber however. Here are the reasons why:

1) The 5.56 round has a length .002 longer than the .223 round.
2) The 5.56 round has a slightly steeper shoulder angle.
3) The military 5.56 brass depending on make is thicker and exceeds pressure
NATO specification 5.56mm ammunition is loaded to a pressure that exceeds standards set out by SAAMI guidelines for it's civilian twin, the .223 Remington. While use of either commercial or NATO specification ammuniton is safe to use in the AR15/M16 series rifles, the use of NATO specification ammunition in other firearms may result in excessive chamber pressure.