How does genital surgery (commonly called sex reassignment surgery) work?
Surgery doesn't define you as trans any more than it defines your gender. Although there are no end of people who might portray trans women (a trans woman, by the way, is someone who transitioned from male to female) as super-gay or trans men as super-butch, it just ain't so.
Everybody involved has warm and tingly parts, and they do what comes naturally to them. Going forward, you can skip this question and questions about the state of someone else's genitalia; it's their business, not yours.
The way they present themselves to you and the world is what matters. Are trans people part of human history, or just a recent phenomenon?
Maybe you have a new coworker who's transgender or your friend's sibling just came out as trans.
Whatever your point of entry, you have questions about transgender people.