C-Print originally refereed to:

KODAK COLOR PRINT MATERIAL Type C. This was a fiber based color paper in the late 50's. It was processed in KODAK COLOR PRINT PROCESS P-122. The process took 42 minutes at 75F plus drying including ferrotyping if you wanted a glossy surface.

I am not sure of the origin of the Type C designation. It could be chromgenic since it is indeed a chromogenic paper. I expect it was just selected as a designation rather than actually standing for anything.

through the years type C has become almost any color reflection print.