Hmm, yeah, could use a bit of clarification there, I suppose. Especially since we have "trans*" which covers transsexual and transgender individuals, but only transsexual is actually defined and only then briefly and is ordered with TS as the primary term rather than transsexual.
I know some included genderqueer and genderfluid as transgender individuals and others don't, so no idea on that account.
I'm pretty sure though that transsexual covers MtF and FtM individuals, individuals born with the bodies of one sex but with the mentality and emotions/sapience/spirit/soul(pick your favorite term for the part of us that does the metaphysics) of the other. Generally implied to be on the path of transition or to have already transitioned, IIRC. Also rendered as transmen and transwomen as the longer form of FtM and MtF, respectively.
Trans by itself, I believe, refers to these individuals, though as always, context can modify it so that even if it's just "trans" rather than "trans*" it could mean whathaveyou.