Why is it called .223, if the bullet is actually .224? Why is the NATO counterpart designated as 5.56 when .224 technically converts to 5.69?

Why is it called .223, if the bullet is actually .224? Why is the NATO counterpart designated as 5.56 when .224 technically converts to 5.69? via DoubleTapper http://ift.tt/2luYXZG