"Inkjet" is a tell nothing term. Pictorial Art (subjective as it is) is most commonly described as the medium (Oil, Watercolor, Silver Gelatin, Gum over, Platinum/Palladium, Carbon, etc.) it stands to reason that "Pigment Ink" is as accurate a description as you are likely to get. That's my two cents, that and that people buy prints when they like how they look, and collectors got over the whole thing years ago. That said, a person can call their own stuff seedless watermelon if they like, although it says even less than "Inkjet".
Sometimes it is taken a bit further and the substrate is included, for example “Platinum Palladium on Arches Platine”. Personally I think think that with digital printing that the paper is an important part of the description, because you can’t really tell the difference between a high gloss baryta and a cotton rag paper by the image on a computer screen. It help gives a more knowledgeable viewer a better idea of the print.
I think it is important to realize that once something is printed that it is no longer an image, but a physical object that carries an image. It behooves us as photographers to be accurate and mindful of what we produce, particularly now that image making is an everyday practice of almost everyone. Now more than ever prints matter, precisely because they are physical art in a world of digital noise.