hermaphrodite is an organism of a species whose members possess both male and female sexual organs during their lives.
In humans hermaphrodites do not exist, however, Intersexuals do
An
intersexual or intersex person (or organism of any unisexual species) is one who is born with
genitalia and/or secondary sex
characteristics determined as neither exclusively male nor female, or which combine features of the male and female sexes.
And no, they dont have a penis and a vagina. Its usually an awkward mix.