OK, tranny time.
Drag queens: guys who dress up like women because it's fun. They usually look pretty extreme; huge wigs and crazy makeup etc. Like the clowns at gay birthday parties, they're the life of the party. Think "celebrity trapped in a normal person's body"
Transvestites: Guys who dress up like women (and vice versa), usually in the privacy of their own home and as a sexual thing. More of a kink thing.
Transgender: people who feel like their biological sex doesn't match their perception of who they are. Think man trapped in woman's body. They usually dress in accordance with their mental images of themselves. Sometimes on horomones.
Transsexuals: people who've had sex-reassignment surgery.