...how the creator got from A to B is the backstory...
Certainly with inkjet printing, becasue there is no backstory with respect to the actual (physical) printing of the image. Well, that's not quite true, it usually goes like this: "I put a piece of paper in the printer, loaded its icc profile, and hit the print button in photoshop". For other printing techniques there is a 'backstory', or biography, that is relevant, interesting and important to the buyer/collector. Have a look at
http://www.photogravure.com/ to see what I mean. Maybe one day there'll be a similar site called
www.epsonultrachromek3inkset.com, but I doubt it.
...but know what they absolutely need to know in the course of a few words.
So "Pigment on (xyz media)" is ok (but misleading), while 'inkjet pigment print on (xyz media)' is too long-winded (but accurate)?
It's interesting why many photographers are jumping through hoops to avoid using the word inkjet. I suspect it has something to do with the perception of the work's value by the buyer/collector/viewer, but I may be mistaken (oooh, it's a giclee print - must be worth a lot more than a plain old inkjet pigment version. Doh!) However, if that is the case then it's a shame, because a strong image will always sell, pretty much no matter what it's printed on or how it's described. If you've got confidence in the strength of your work spell it out - 'This is an archival inkjet print on Epson matte paper made using the Epson Ultrachrome K3 inkset'. If on the other hand you work is of average quality, dress it up in some fancy language - 'This is a giclee carbon (pigment) print on 100% acid-free organic fair-trade cotton rag' - and hope the gullible buyer falls for it. I wouldn't hold my breath though.