Dating a drag queen, a transsexual a shemale or a ladyboy
"Shemale"
A term describing a male-to-female transgender person who intentionally retains their male genitalia, while surgically and hormonally transforming the rest of their body to appear as feminine as possible. Typically these individuals pursue a career in some part of the "sex industry".
PLEASE NOTE, this term does NOT necessarily apply to all NON-OP trans-women, and there are MANY who take great umbrage at being referred to as "shemales", particularly from those outside the trans-community, much the same as most black people resent the "N-word".
"Transsexuals" are those who either are, or have serious intentions of, living full time, 24/7, as the gender opposite of how they were born, due to a profound conflict between what is in their hearts and minds vs what is between their legs.
For a wide variety of reasons too complex to go into here, not ALL transsexuals will undergo gender reconfiguration surgery (GRS), but that does NOT make them "shemales".
"Ladyboy"
It's a slang term specific to ethnicly Asian transsexuals, due to their typically youthful appearance.
Then there is the old "umbrella" term - TRANSGENDER - which can be safely used without fear of offense for pretty much ALL OF THE ABOVE catagories, although individual results may vary.