What is the difference between the 6mmTCU and the 6mm-223 or is it the same round?

It is NOT the same. The 6mm-.223 (aka 6x45) is the .223 simply necked up to 6mm with no other changes. The TCU is a .223 necked up and fireformed to minimum body taper and a sharper shoulder, resulting in a slight gain in capacity.

The usable difference is not detectable in the field. The main reason for the TCU is that the nearly-straight case walls grip the chamber better and thus are better suited to single shot pistols -- not to mention backthrust considerations against the frame of the Contender.