All I know is that I love anyone (with a preference for women) regardless of gender. I would say gender does matter to me since I prefer women, but I would love anyone regardless, and would gladly date women, men, and everyone in-between. not only this, but if my love transitioned, I would still love them.
I think pan is regardless of gender. Bi is your own and any other gender that is different from your own (essentially what you said), and omni is all the genders (but because of the gender they are, not regardless.)
its all semantics honestly, but I don’t think many people who identify as any of these would be actually strictly adherent. Sexuality is a spectrum after all.