Can 5.56 x 45 and 223 ammo be interchanged?

.223 Remington ammo can be safely cycled through a 5.56x45 chamber - 5.56x45 ammo should not be cycled through a .223 Remington chamber. Both types may be cycled through a .223 Wylde chamber, but .223 Wylde may only be cycled through a .223 Wylde chamber.