Lots of threads on this in this forum if you search. Here is one that is about a week old that should give you some of the information you are looking for:
For ME..On FACTORY LOADS--I shoot 5.56MM ONLY in my AR's that are marked 5.56 on the barrels==NOT in my Remingtons that are marked .223 Rem. on the barrel.
^^^This point, for me is moot anyway, since I MOSTLY fire my reloads through either weapons.
With this in mind, my AR loads ARE a little "Hotter" than the loads that I fire through my Remingtons.
I DO think that the chambers marked "5.56" are designed for a higher pressure than chambers marked ".223 Rem."
This "Thinking" is worth what you paid for it....
As to the OP's question-YES-ALL of my .223Rem./5.56MM rounds get loaded with dies marked ".223Rem."....Bill.