You can shoot a .223 round in a 5.56mm chamber, just not the other way around. 5.56 is loaded to a higher pressure and could cause a rupture of a .223 chamber.
The .223 Wylde chamber can fire both the .223 and 5.56.
Check out the Ammo Oracle on
www.ar15.com. Good source of information on the AR-15 as well as all types of ammo.