My understanding is that Drag Queens love to dress up as men portraying women. The following morning, they are delighted to go back to being men. It's an act or a show for them. One whom I know personally views it as a way to entertain and make money. He's very good, but he's a guy and makes no bones about it.
Transgenders are those who like to dress up, but don't care to follow it through with surgery or permanent changes to their body. If they can live, even part time, as female, that's good. They like their male bits and want to keep them.
Transsexuals despise their male parts and want them gone. A Transsexual is one who seeks permanent, physical changes to their body in order to bring their body appearance in line with their mental identity of being female. They want no part of being a male.
This is an over-simplification, for purposes of a quick explanation. There are many degrees in between. This is what I've been told.