Yes, the thicker case for the 5.56 means pressure will be higher than a similar charge in .223. If you reload a max .223 charge in a 5.56 the pressure will high enough that you may get a case rupture.
And primers blown out the case which wind up rattling around in your receiver.
As well as higher pressures the 5.56 cartridge has a slightly longer case neck. The bullet is supposed to make a short `jump’ before engaging the rifling in the barrel. A barrel with a 5.56 leade allows this to happen.
A .223 barrel has a slightly shorter leade, so the bullet from a 5.56 cartridge leaves the cartridge then immediately engages the rifling which confuses it, so it becomes angry with you and puts your eye out.