Not sure there is an official by Yoshi or the Devs what the current gear we have is called honestly. I'm pretty sure somewhere in one of the AF quests it's called Artifact armor or something.

Any who... I go by this little formula and I know most FFXI people do too.

Artifact Armor(Quested lvl's45/50)=AF1
Relic Armor(Acquired by Myth. Tomes.)=AF2/Relic
Mysterious "AF2" Armor shown by Yoshida(The below image)=AF3


Is it following your or the Devs/Yoshi's logic? Probably not, honestly just call it what you want. As long as others understand what you're talking about, what does it honestly matter?