The chamber pressure is measured differently (CUP vs. PSI) but the 5.56 is a bit hotter than the .223 Rem. You can always use .223 in a barrel chambered for 5.56 but shouldn’t use 5.56 in a .223 barrel. The .223 Wilde chamber is a compromise and can fire both.
“The .223 Wilde chamber is a compromise and can fire both.”
I have a 20” RRA heavy barrel with a Wilde chamber. It shoots everything I’ve fed it accurately.