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.