Transgender is a term used for people who do not fit the gender role assigned at birth (male or female), as well as the role traditionally held by society.
Sex Does NOT Equal Gender:
People often get these two terms confused because they are similar yet in reality they are entirely different. Sex is the biological genitalia we are born with, either male, female, or intersex(combination of male/female genitalia). Gender is how we identify and is a social/biological construct, so one may have the parts of a male yet their mind, body, and spirit identifies as a female.
The Gender Continuum:
Like sexuality, gender identity lies on a continuum. Most people identify with the gender corresponding to their biological sex of male or female. However, some people fall along this continuum. For example one may be fully comfortable in their female gender identity but they may exhibit more masculine traits. In reality there are as many genders as there are people on the planet, we each view ourselves and our roles differently and there is no unifying code of gender.
Transgender is an umbrella term for people exhibiting gender variant behavior and is used for transvestites, drag queen/kings, transsexuals, and sometimes genderqueer.
Transvestite-Someone who wears the clothing of the opposite sex (AKA - Crossdresser). An individual whose gender identity may or may not match their birth sex.
Drag Queen/King-A drag queen is a biological male who impersonates a female, and a drag king is a biological female who impersonates a male. Drag is usually done for entertainment purposes and does not necessarily reflect the persons desire to live as a male or female.
Transsexual-A person who desires to live as the opposite sex. Some choose to undergo elective surgery or take hormones to have their sex match their gender identity. Pre-operative Transsexuals are those who have not undergone surgery. Post-Operative Transsexuals have undergone surgical procedures. Non-operative are transsexuals who choose not to undergo surgery. Most transsexuals who have transitioned classify as male or female but some identify as transman, or transwoman.
Genderqueer-Individuals who self-identify as gender queer may consider themselves to be both male and female, androgynous, being neither male or female, or falling completely outside of the gender binary spectrum.
Sexual Orientation Does NOT Equal Gender Identity:
Sexual orientation and gender identity are two completely separate concepts. Transgender people can be gay, straight, bisexual, or asexual. Just the same that gay/lesbian people may have no issue with their gender identity and their gender fits their biological sex. One's gender identity or sexual orientation has no influence on the other.
This is the fear of gender variant people. Many people do not understand transgender people and are disgusted, scared, or don't understand, instead of seeking to educate themselves on the topic they look to harass, tease, or physically cause harm to trans-folks.
National Center for Transgender Equality
Sylvia Rivera Law Project
Sylvia Gender Public Advocacy Coalition
International Foundation for Gender Education
Transgender Awareness Videos (20/20 Video 1-5):