Welcome to DPUG, and welcome to one of the biggest bones of contention in the digital world, aside from brand vs. brand fanboys.
Note, I'm just a hobby photographer, I don't sell my work, and it's not in museums or galleries. But...
I think that "Pigment Inkjet Print" (or "Dye Inkjet Print" if appropriate) is sufficient to identify the medium. If I were in such a position, I would probably include some additional metadata on a tag on the back of the print as to Printer/Ink type and substrate details, perhaps date of printing...these should be provided and known to the buyer, but I don't think it's necessary to have all the "nerd stuff" out front.
"Archival" is a word that is somewhat subjective and ill-defined, and despite the good work that the folks at Aardenburg are doing with fade testing, inkjet prints just don't have the long track record that more traditional output media do, so it's tough to justify a claim of "archival".
But really, it's the wild, wild west out there. There's always the favorite "Giclee", and one 3rd-party B&W inkset manufacturer spent some time calling their output "carbon prints" because they used carbon black pigments, despite the fact that it had nothing to do with traditional carbon prints (aka carbon transfer prints), and another (perhaps the same?), spent some time referring to their output as "Digital Platinum", because the tones of the inks used supposedly mimicked platinum prints.
IMO, it's important to be honest about the origin of the print, because the more we try to obfuscate, the more it lends credence to the idea than a "pigment inkjet print" is somehow not valuable, and that an inkjet print that uses some flowery language to describe it is somehow more valuable. I can call a dye inkjet print form a $49 printer a "Giclee" but that doesn't mean it won't be faded in a year. And, even more IMO, if your gallery seeks to obfuscate the nature of the print, perhaps you should re-consider your business relationship with said gallery.
Okay...time for someone else to hop up on the soapbox.
--Greg