Transsexuals are the same (psychologically), but they have physically taken steps to alter their sex organs.
Male transvestites (cross-dressers) wear female clothing and makeup-- it has less to do with any gender confusion and more to do with the sexual thrill.
This, of course, is not to be confused with androgyny. Examples of those with androgynous traits (those whose looks or builds makes determining their gender difficult) are Michael Jackson, Boy George, David Bowie, k.d. lang, Prince, Marilyn Manson, Pat (Saturday Night Live), etc.
Excuse me now. I've got to take a shower.
"A transgender rejects the gender that society has assigned..."
They also reject: Sun rising in the east, 1 + 1 = 2, and in this case, apparently, legal speed limits.
Unfortunately for them, society doesn't assign "gender roles" (although some try in varying degrees to perversely re-assign them). Nature (and nature's God) take care of gender at the level of the chromosome.