The 5.56 has thicker case walls, meaning reduced powder capacity, the 5.56 has a shorter throat than a .223 chamber. A .223 is pressure tested SAAMI style in the middle of the case, where pressure readings are highest. The 5.56 chamber pressure is measured from the case neck ( might be wrong but I think that is a military method) where the pressure measured is lower than the mid point, and the 5.56 is still measured higher than a .223. Put a 5.56 in a .223 chamber and you could get dangerously high pressures. Most guns will take it and you won't notice until some number of rounds later and the metals in your gun have had all the beating they can take. You might lose some accuracy one way or the other, but the concern is high chamber pressures.
Scheme well, scheme often.
Please add "In My not so Humble Opinion" to the end of all my posts. Thank you.