Better, I think, to educate gallerists and customers than perpetuate some of the silly labels. I don't really care what others call their prints, but I will contest any inkjet I encounter that is labeled a "carbon" or "pigment" print, since those terms historically refer to carbon transfers and so are just plain deceptive.
Hence why in my suggestion it includes the word "Giclée".. as in "Pigment Giclée on Cotton Rag", as an example, and silly labels, well, each to his own on that one...
EDIT:
-Customer: " It says inkjet, how can it be it cost 400 euros, I can buy 10 inkjet printers for that price!!"
- Gallery: "Oh, no it's not the same thing, these inkjet prints are made on a high-end extra quality top notch inkjet printer using a special photographic long duration ink, it's far from those printers you see at the mall"
-Customer: "Really... oh well, let's see what you have in the other room instead"
Hence, "Digigraphie" or "Giclée" ...