There's true color case hardening, and then there's color case "hardening".
True color case hardening is typically a bone charcoal color case process which has the definite purpose of case hardening the steel (iron in the old days), with the color being a byproduct. The bone charcoal imparts extra carbon to the surface of the metal to harden the surface, while the core remains relatively ductile. This process was meant to be used on iron frames, and carried over into the era of steel frames. It is a true case hardening process, as intended.
Bone color case hardening can also be done to a lesser degree, more for the cosmetics of the colors, when the underlying steel already contains sufficient carbon. The lesser process produces colors that are not as durable, and one will find that those who offer such services will often clear coat the colors to protect them. This is still color case "hardening", but barely. It is a relatively safe process to use on small parts made of steel having high carbon content, as a true color case hardening put on such parts will usually cause them to become brittle and crack.
There is also a cyanide color case which is designed to similate the colors of the more expensive and labor intensive bone color case. I don't know if the cyanide process imparts any surface hardness. It is my understanding that this process is more cosmetic than anything. Most of the Italian imports have this finish.
I'm not sure how any color case hardening, even true bone color case, compares to plain case hardening, or why which process is used for what.