A c-print is a "chromogenic print" or an ordinary wet print from a color negative (usually). This would include digital prints on the same paper, like Lambda, LightJet, and Chromira prints on Fuji Crystal Archive, even if they are from transparencies or digital originals.
Cibachrome/Ilfochrome prints are NOT c-prints. Cibachromes in gallery-speak are "dye-destruction prints."
Here's a good glossary of many of the common terms--