There has been over a 100 years of usage where the term carbon print refers to a print that is created from ink or pigment suspended in a gelatin tissue that has been made light senstive through the application of a dichromate. This tissue is then exposed via contact printing with UV radiation, which hardens the tissue in proportion to the amount of light transmitted through the negative. This tissue is transferred either to a temporary substrate or a final substrate, and the unhardened gelatin is then 'developed away' with hot water. The varying thickness of the remaining hardened tissue creates a photographic image on the substrate.
If Clyde has figured a way for his inkjet printer to do all this, then by all means, call the results a carbon print. And I sure would like to see that printer!