Like Shelly I also feel in between genders. My body is male, but I have some more feminine features. My personality is androgynous--I have both typically masculine and typically feminine behavioral traits and emotions. Behavior and emotions are as much social as physical. I suppose that one of the reasons I like to dress en femme is to be able to give some physical expression to the feelings that I have. In that sense, when I put on a skirt I bring out the woman in me. But whether I am wearing pants or a skirt I am the same person. That person is neither purely male nor female, but is a bit of both.
Etymologically the terms "crossdresser" and "tramsvestite" mean the same thing. "->-bleeped-<-" is just the Latinized version. The connotations of the terms have come to be somewhat different, largely due (as Deb points out) to the psychological association between transvestitism and sexual fetishes.