The Ludicrous Labour

[Pavlov]

I'm confused. Is a "trans woman" a female to male transsexual, or a male to female transsexual?

Trans woman: male to female.
Trans man: female to male.

So, a "trans woman" is someone of the male sex (a man) who "transitioned" to the female sex? 

And a "trans man" is someone of the female sex (a woman) who "transitioned" to the male sex? 

But how do they do that? I mean, even if they have an operation, it doesn't change their sex, it only changes their appearance. It's still a man, a male. The operation changes neither their sex, nor what they think they are.