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.