Generally, 5.56 barrel chambers will be throated for longer heavier bullets than most .223 commercial ammo.
Generally though you really ought to check with the manufacturer, because some barrels marked .223 are actually chambered to accept 5.56 as well as .223, while most .223 barrels especially older .223 barrels are chambered for the shorter, lighter bullets originally loaded in commercial .223 ammo.
I suspect that the only difference in firing pins is between early ARs that were semi-auto versions of the M16, and current ARs designed as semi-auto from the get-go.