According to the Transgender Safe Zone Resource Manual provided by UC Davis's LGBT Resource Center, "transgender" generally describes a person who does not identify with the common manifestations and expressions of gender associated with his or her biological sex at birth. For example, a transgender woman may not identify with society's perceptions of femininity and instead express more masculine behaviors.
The Manual explains that a transsexual person is one who also misidentifies with his or her biological sex and may seek to express a different gender. However, the term "transsexual" suggests that the individual has chosen or is considering to have sex reassignment surgery.
The term "transvestite" is very outdated because it technically only refers to the act of wearing clothes that are associated with the opposite gender and sex. For example, a man wearing high heels would have been characterized as a "transvestite" in previous decades. However, as soon as he takes off the heels and returns to wearing men's attire, he would no longer be considered as such.
Many people in the American LGBT community do not use "transvestite" because it still carries negative connotations. The terms "transgender" and "transsexual" are widely thought to be more politically correct and respectful to the fluidity in gender expression that many "trans" people experience.