In order to understand the difference between someone who is gay, lesbian, or bisexual, and someone who is transgender, you need to know the difference between sex and gender. Simply put, sex is polarity of anatomy, gender is polarity of appearance and behavior. As one gains familiarity with transgenderism, these definitions quickly break down, but they serve as a good starting point.
Most people think there are just two sexes, male and female.
Such is not the case. People who are intersexed and people who are transsexual constitute sexes which are neither exactly male nor exactly female. Gender is exhibited by countless signals, from articles of clothing to cosmetics, hairstyles, conversational styles, body language and much more. Women have won for themselves the right to a wide range of gender expression. Men have not made a corresponding effort.