?
Transgender is an umbrella term for people whose sex and gender are inconsistent with eachother. 'Transgender' can cover all sorts of identities, not just MtF and FtM. Genderqueer, agender, bigender, third-gender, genderf**k and basically any non-cisgender (sex and gender matching) gender identity falls under the transgender umbrella.
Transsexual, from what I'm aware, is a more specific term to describe someone who is in the process of/has completed the process of transitioning from one sex to another, although I've heard it used by people who aren't transitioning. (Judging by Clones' answer the reason for that is that people who are MtF or FtM transgender can use 'transsexual' interchangably with that. Finally I learn. :D) There seems to be a general confusion over this even between people who are sure they know what they're talking about...
@Marjorie: You appear to be confusing 'transgender' with 'cross-dressing'. ^_^
Hopefully this has cleared it up for you! :)
Leon