No, that's not what intersex is. Intersex is a range of different secondary sex traits, genitalia, or hormonal imbalance. It's not necessarily only genitalia as those are not the only markings for a sex. Id recommend watching The Octopus Lady's video on Clownfish where she goes into what intersex exactly is bc ppl tend to correlate the way clownfish change sex to transgender and intersex ppl
Adding on, having the genitalia of the opposite sex doesn't always mean it will be fully functioning. An intersex person who has a vagina could also have underdeveloped testes, an overgrown clitoris becoming a pseudo-penis but lack testicles, could be a major hormonal imbalance of testosterone-estrogen that, in a female, would cause her to look more like a man. Intersex people are as vast as it comes and honestly it's super interesting, some people might go their whole lives not knowing they're actually intersex!
Iltak is prolly intersex or something like that atp lmao