Perhaps fine art prints could mean it is up to gallery or museum standards? They started accepting C-Prints as a legitimate medium decades ago, so any Fuji Frontier, LightJet, LED, Durst Lambda, or other RA-4 process prints would qualify.
As far as inkjet, Giclee prints have gained acceptance, but standards are a bit vague. There are acid free 100% rag paper inkjet papers available, but what about the OBAs (optical brightining agents) used in the paper? What about the clay coatings these papers have? Supposedly they are buffered/nuetral. Inks? Epson pigment inks claims quite a high longevity. However, many folks seem to agree that a print made on such a paper with pigment inks meets the criteria of a fine art print.
And there are other types of digital printing methods as well. Dye Sublimation, Iris, etc.
But as far as just prints? Perhaps that is any old inkjet print of unkown paper, ink, etc. I make proofs and other prints that really only need a short life with cheapo papers like Premium Lustre, HeavyWeight Matte, etc. And if it comes out of one of my dye ink/office type printers, who cares then?