As BC said.
Case hardening is just what it says, a process that imparts carbon into the surface of the steel, resulting in said surface (the case) being made much harder then the material underneath. Formerly much used on low quality steel or in some cases wrought iron. With the advent of alloy steel the expensive and time consuming extra process was omitted and we went with a plain blue finish. The colors result from the chemical residues on the surface from the material used to embed or soak in the carbon, in the case of guns, usually charred bone or leather.
Real case hardening is quite wear resistant, but the colors will rub off, they're just surface discoloration, see Turnball (?) firearms for really good examples.