trans | ???

alright, i've always been confused about the exact definition of a transgendered person. can anybody help me out? yesterday i started my sociology class, and the teacher was talking about the different ranks of sexes. of course on the top was male, and then on the bottom, people said "female" but she corrected everybody and said it'd be the transgendered. nobody knew what it meant so she told them that it meant a person that had a sex change. i didn't think she was completely right, but since i don't KNOW the exact answer... i didn't wanna speak up. it kinda bothers me if people have the wrong definition of it. i just thought a person that had a sex change was a transexual?? please help!