If you’ve ever wondered about the differences between 5.56 NATO and .223 Remington, well, this article gives a good account of the differences.
Bottom line is, if you’ve a .223 rifle, do not fire 5.56mm from it. If you’ve a 5.56mm rifle, you’re OK (but may see some inaccuracy due to the added “slop”, the slop being an allowance to ensure the firearm will fire when dirty/grimy).