From what I have always thought and learned, a trans-sexual is a person who is in the middle of transferring their sex from one to the other. This is because they really think that they are in the wrong body. Once the final surgery has been performed, they are a member of the other sex. A cross-dresser is a person who has no desire to switch sexes but who gets off on dressing up in womens clothes.

"boys will be girls and girls will be boys, it's a mixed up, jumbled up, shook up world that we live in" (The Kinks-Lola)

Barton.