You're semi-correct.
Futanari (Futa) is the Japanese word for Hermaphroditism, ふたなり: Of two kinds.
What this means is a Futanari character if going by the Japanese term is a female with BOTH a Dick and a Vagina. Over time this became blurred as the term now is used derogatorily or as a general tag for content that features a female with a dick. The scrotum does not need to be present in this term, as of the earliest forms swap between internal testes, not explained at all or has full scrotum.
If the female has both a vagina and a dick then traditionally she is a 'Futanari'.
If the female only has a dick then the term would be 'Dick Girl'.
If a character is a male that presents themselves as feminine to attract other males intentionally then they are a 'trap', vice versa.
If a male dresses and acts feminine then they are a 'femboy'.
Characters who don't conform to traditional gender norms are 'tomboys'.
A male who identifies as a male but gets degraded and dominated would be reffered to derogatorily as a 'sissy'.
These terms have nothing to do with transexuals.