Long before digital photography was thought of, or Photoshop was more than a vague notion in the Knoll Brother's minds, there was even then a problem of description for photographic prints. A huge gulf of quality lay between a print produced by the like of Adams and Weston on Agfa Record Rapid or the old Ilford Galerie, and your average consumer print churned out by the local chemist or the mail-order lab on cheap, thin, resin-coat paper. Yet they were all photographic prints. Those of us "staring into trays" knew the difference, but your typical weekend snapper did not, and cared less.
We have exactly the same problem now. The notion of "ink-jet" as a description became pejorative because of its early association with poor-quality dyes and print life measured in months, not years. We still have not managed to shake this perception off, although the best printers with the best pigments on the finest papers can produce work which has the depth, quality and longevity of the best silver prints.
Museums and galleries which are well-informed and passionate about their material do know the difference, and so do the relatively small number of serious buyers of art. We don't have to invent silly new pretentious nomenclature to impress them. On the rear of my prints which I consider fine enough to be bothered mounting for display, I simply annotate with the subject, date, paper make and type, and the inkset (Epson K3 in my case). Those who know about this stuff will appreciate the information, which is all that counts.
John