This should help.
A .223 chamber has a shorter leade, or free bore, than a 5.56 chamber. It's theoretically possible for a heavy (longer) bullet in a 5.56 round to be jammed in to the start of the rifling in a .223 chamber. This could theoretically cause a over pressure situation. The bullet needs to have a short free space for it's initial movement.
I use "theoretically" because I don't see any reports of this happening, and a lot of peeps use 5.56 in .223 chambers.
Commercial .223 brass can be thinner than 5.56 NATO brass. The NATO brass may have a smaller volume than .223 brass.