As someone who isn't trans, I view it as a medical condition that can become an intrinsic part of a person's identity, or it may not. My closest trans friend is FtM, and being a transman is part of his identity. He refers to the female identity his parents tried to force on him as his deceased conjoined twin. He is mentally male, but the journey towards finding himself was a big thing, and he does take a lot of pride in not just being a man, but in being a transman. It comes off more like the example of being deaf - a medical condition that is also part of a large, vibrant community.
I have met transgendered people who do not view it as part of their identity. It's a medical condition that they want corrected - it's an inconvenience that exists. Instead of being deaf, I guess it would be more like being born with polydactyly (not trying to be insulting in any way, just the best analogy I could come up with). It doesn't change who they are in any way, and there isn't really a polydactyl community. It's just something you have, and you either get it fixed surgically or you don't.
So I guess the answer from someone on the outside looking in is Either or Both?