everything i have named is a real kind of intersex condition but there’s over a dozen types/i don’t know all their names off the top of my head. ambiguous genitalia is typically how intersex individuals are diagnosed so i suspect there’s a few different conditions that produce it.
the point here is that nature produces people who exhibit characteristics from both phenotypes and often can still reproduce. bimodal but not a binary. some people really do have both. so insisting on a strict binary is (drumroll) a social construct. there are two, but also a spectrum
There are no people with both vaginas and a penis. That does nto happen. You do not know what you are talking about.