A gunsmith friend tells me there are at least one dozen different 5.56mm/.223 chambers. Here are some: Click on reamer dimensions:
Commercial .223 brass can be thinner than 5.56 NATO brass. The NATO brass may have a smaller volume than .223 brass.
Since 1968 i've been weighing the cases for my accuracy loads. Some British made 5.56mm military brass is very thick. US military 5.56mm brass is not heavier/thicker than .223 made commercial brass. The heaviest US made cases are Federal Gold Medal. The heaviest cases of all are those made by Lapua.
Click on brass weights:
This young man did some fine research:
Since 1968 i have fired at least a half million rounds of US military M193 5.56mm ammunition in the .223 chambers of numerous guns with no ill effects. Some of my guns have been re-barreled five or more times. i would not attempt to fire a US military 5.56mm round in a .223 match chamber.
i'm not suggesting that you fire 5.56mm ammunition in the chamber of your .223 rifle.