Transsexuality is a condition in which a person feels a strong and persistent desire to live and be accepted as a member of the opposite sex. This desire is usually accompanied by a strong feeling of discomfort with, or inactivity of, one's own sex. A transsexual person usually undergoes hormone therapy and sex reassignment surgery to align their physical appearance with their inner sense of gender.
Transgender, on the other hand, is an umbrella term that refers to individuals whose gender identity or expression does not conform to that typically associated with the sex to which they were assigned at birth. Gender identity is a person's internal, personal sense of being a man or a woman (or boy or girl). Gender expression refers to the way a person communicates gender identity to others through behavior, clothing, haircut, voice, or body characteristics.