As I understand it, the two terms are interchangeable except in medical terminology where transsexual refers to people who have drug therapy or surgery to better align their bodies with their innate gender and/or self-image. Transgendered is more a general term describing a person at odds with the gender he or she was assigned at birth.
Some transgendered people simply seek more fluid gender roles. Some cross dress. Some live as the opposite sex. Some do drug therapy. Some have surgery. Some do all of the above.
Transgendered people are born male, female and intersex. Being transgendered or transsexual doesn't have anything to do with sexual preferences. Like the rest of us, they may be gay, lesbian, straight, bisexual, asexual, pansexual, or whatever.