Omega Weapon?

[Alberel]

For the record, they just called it "Omega", and not "Omega Weapon".
While related (and given FF-lore), they're different contraptions.

We don't know that yet. The Weapons were Allagan devices built to fight primals and we've been told that Omega was actually built to fight Bahamut. It's presumably how they trapped him within Dalamud in the first place. Given that both were built to fight primals, Omega may indeed be a Weapon...