A hermaphrodite is a person who is born physically both female and
male. Since no one can reproduce as both a female and male,
"hermaphrodite" isn't used professionally. "Pseudohermaphrodism" refers
to some kinds of intersex. Non-professionally, many people use
hermaphrodite to mean any intersex person.
It can also be used loosely to refer to intersex animals or entire species which reproduce as either female or male.It can also be used to a mythic person who is actually and biologically fully female and fully male. I use the term androgyne for this meaning.