Some are some aren’t. It’s probably closest to the mid 20th century American concept of transvestite, which at the time encompassed everyone from transsexuals (at that time the medical definition of transsexual required what we would today describe as severe dysphoria and exclusive Heterosexuality) to the more modern definitions of trans people, both binary and nonbinary, as well as cisgender crossdressers of all varieties. Source
Transvestite prescriptively means a crossdresser, by the way. Literally, that is. "-vestire “to dress, to clothe” (from PIE *wes- (2) “to clothe,” extended form of root *eu- “to dress”).
I’m not gonna argue over how the terms was used in mid 20th century America, I wouldn’t know. Just like etymology, don’t mind me.
Oh absolutely, and it meant that then because sexology was in the process of catching up with groups of people that medicine had recently gained the ability to make the differences between far more significant. They were also very prone to medical gatekeeping and treating transition as the absolute last resort for those unable to live a normal life as their assigned gender