I do think your example of pretending to be one specific other person is different. That does go to consent, because if someone is only up for sex with one specific person it's a bit different from only being up for sex with a certain type of person.

That's an interesting distinction, which I'll have to think about.

I'd think passing yourself off as being of the other gender pretty much counts too..

Counts as what? (If you're referring to trans people, then I should mention that not mentioning you're trans is no more "passing yourself off" as something you're not than is not mentioning you're cis. Trans men are men, and trans women are women. My previous post was aimed precisely at exposing the cisnormative assumptions in discussions around this kind of issue.)