There's no practical difference between 5.56 and .223. Used to be that some older guns chambered for .223 possibly couldn't handle 5.56 ammo, although I've never seen any proof of this. Unless you are buying an older rifle specifically marked .223, I wouldn't worry about it.
As between 38 special and .357, there's a world of difference. I wouldn't want to see what a cartridge with the same full power of .357 would do to a gun made only for .38 special (if you could somehow cram such a cartridge into a .38)