What is the difference between "transgendered" and "gender-queer"?

[Weasley: My Anti-drug]

I'm writing a paper on LGBT issues, and I'm not sure if there is a difference (or if I should include) "gender-queer". I'm a little unclear of the borderline between the two terms, or are they the same?

Thank you!
...and what is the term used when you don't ascribe to any gender?