I just call it Relic gear since it shares the same set names with it's FFXI counterparts.

I think the problem comes in where people denoted AF2 and Relic as the same thing in FFXI:

AF1 = Artifact
AF2 = Relic
AF3 = Empyrean

Some others also denoted AF1-5 as the pieces of Artifact gear (five in a set in FFXI) themselves as well, adding to the confusion. In later years, SE tried to clear up the confusion by outright calling the sets Artifact, Relic, and Empyrean gear.

So my guess would be:

Artifact
Relic
Artifact v2 (AF2)
... etc