The 5.56 vs. 223 debate has been going on for years and would fill volumes.
I can only say this: the actual outside dimensions, overall length and such are exactly the same. Where you get into differences is in the thickness of the case walls.
Typically I throw all LC and other military brass, staked and crimped primers in one bucket. And commercial 223, Rem. Win. and so on in another.
If you're loading hot, or near hot loads in say Remington commercial 223 brass. And you load a Lake City or whatever 5.56 case with same hot load you could have an issue with pressure due to the thicker walls/less volume in the military brass.
Short answer it's best to sort brass for high powered rifles and work up loads slowly and carefully.