Omega Weapon?

[Torquil]

This.

Omega Weapon is usually an improved version of Ultima Weapon, while Omega is an incredibly powerful robot.

I think you're reading too much into slight translation variations. Omega or Omega Weapon, it's all the same recurring reference, a super powerful (generally optional) mechanical boss. In some games there's a direct reference to a related Ultima Weapon (FF8), in some games it stands alone (FF5). Either way, it's the same recurring reference. There's nothing to suggest there's a distinction between an Omega and an Omega Weapon.