Trans is an umbrella term that can be used to refer to anybody who does not identify with or express the gender they were assigned at birth (https://www.hrc.org/resources/sexual-orientation-and-gender-...). Having surgery and/or always presenting as a gender you weren't assigned at birth is not a prerequisite to being trans. "Transvestite" is a somewhat dated term that is considered offensive in some circles, though either way, a transvestite would by definition be "trans".