Transgender, transsexual and transvestite are not the same. Calling a Transgender or Gender-Variant person a transsexual or a transvestite may be very offensive to them. Transgender is considered to be a more politically correct term.
As described above, Transgender is an umbrella term that encompasses a variety of people including MtF, FtM, Gender-Variant, genderqueer, non-binary and other gender identities.
But how does transsexual or transvestite differ from Transgender?
Transsexual refers to an individual who has had undergone medical procedures and/or hormone replacement therapy so that their physical appearance matches their gender identity.
Transvestite refers to a person who identifies as one sex but wears the clothing of the opposite sex. In short, they wear the clothes of the gender they do not identify with. Transvestite isn’t a commonly used term anymore because of the negative connotations with fetishism. Crossdresser is a more widely accepted term.
Drag Queens are not transvestites or crossdressers. They are performers and personalities.
Its important to respect the terminology that people use for themselves. Terminology is changing all the time therefore one cannot assume about how people self-identify. While it is appropriate to ask about someone’s pronouns, they may not want to share details about their sexual orientation or gender identity.