The general consensus seems to be that, for the most part, we still know too little (and the information we DO have is pretty conflicting) about what is the difference between an Eikon and a Primal. In Bahamut's case (an Elder Primal) he was kept in stasis by dragons being kept in stasis plus something else I may not remember right now.
Garuda, Ravana and all the other known Primals need to feed of crystals or the aether from the land to maintain their forms, while Belias-egi throws a whole wrench in it by being an egi based off an Elder Primal with no known tribe (beast or otherwise) to make the original summoning that would have formed him (Belias-egi being a beefed-up Ifrit-egi non-withstanding).
However, the Triad seems weird in that they don't seem to ABSORB aether, but rather RELEASE it. If I'm understanding things right, the Triad were some sort of battery for Azys La, seeing as how at least Sephirot's tribe that would have kept him summoned is all but extinct and 3 primals absorbing the aether of the surrounding area would have guaranteed that all those islands would have fallen long before we got there. I'm taking a shot in the dark here but until we are confirmed as to what, exactly, the Triad IS and how in Hydaelin did Allag manage to bind them, I reckon they are (if the terms are indeed different) Eikons, if simply because not-Primals doesn't have the same ring to it.
Random idea: The Triad were actually bound separately, with Sephirot being either the first or last bound. If first, he's getting released first because the technique wasn't quite as sophisticated for his binding at the time and/or hab been corroding longer than the others, and if the second, because his bounds depend on the other two, and with those weakening, his were the first to fully break.
...and now just wait for someone to completely disprove this lol