Don't want to be excessively anal here - - -
but a "C print" is a color print made from a color negative using dye-coupler technology. The "C" is a derivative of the Kodak chemical process designation, eg, C-41.
Cibachrome (now known as Ilfocrhome) prints are direct positive prints made from positive originals (slides) using an azo dye-destruction chemical process. Kodak has a direct positive printing process that leads to "R prints", or prints made using a reversal dye-coupler process from film positive originals (ie, slides).
Yes, a "C print" can be made from a digital original if a negative is produced from the digital file, and then the final print is made using the Kodak 'C-41" process. Likewise, both "R prints" and cibachromes can be made from digital originals if the digital file is first used to create a positive intermediate, which is then printed chemically using either the Kodak R process, or the Ilford azo-dye destruction process.
Originally, after the consent decree against Eastman Kodak in the 50s, they were forced to place their color films and papers for sale without processing included, and were therefore required to make processing chemistry available.
The paper for printing from color negatives was called "Kodak Color Paper type 'C'" and the paper for making prints from slides was called "Kodak Color Paper type 'R'". Just a name, thats all. Later, the same types of paper were called "Ektacolor Paper type 'C'" and "Ektachrome Paper type 'R'".
Later versions included Type numbers instead of the letters 'R' and 'C'. Some of these types were 1910, 1970, 1973 and etc. In fact, the T1970 ended up being called Ektacolor 70 paper and a later version became Ektacolor Plus. The Ektachrome paper family became Ektachrome Radiance paper.
So, that is the history of 'C' and 'R' designations originated by Eastman Kodak.
Generically, it has become to mean prints from negatives 'C' and slides 'R', but it has only been applied to chromogenic papers, not dye bleach materials like Ilfochrome.
Type C Print
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.