Well, if you don't ask, you'll never know, right?
Transgender is an umbrella term that encompasses anyone who doesn't feel like they fit in the gender binary of girl and boy.
Transexual is used to describe someone getting a sex-change *With our without hormones and / or surgery* in order to become a member of the opposite gender that they were not assigned at birth.
Basically, Transexual is covered under being transgender, but not all transgenders are transexuals. When in doubt, go for the umbrella term, or you might upset someone who isn't transitioning.