First of all, there is a range of biological possibilities: typically, XY people have penises and XX people have vaginas. But, there are conditions where a person might be, say, XXY. So there is a genetic question for such people.
Second, the development of sex organs is not an automatic thing based on the chromosomes. It is possible to have a condition known as androgen insensitivity that suppresses the development of male sex organs. This leaves the *default* female sex organs. Often such individuals, who have female external sex organs, do not learn of this condition until puberty (or even later). Again, these are people who are XY and *look* female.
Next, there are the developmental cases of hermaphrodites, where both male and female sex organs are present. often, these cases have surgical 'correction' at birth and are assigned a sex by a doctor.
Next, we have the cases where some more subtle aspect of development is affected and the brain develops characteristics common to one sex while the body develops characteristics of the other sex. It is often the case, for example, in trans-gendered people that the brains show the characteristics of the preferred sex.
All of these are biological, whether genetic or developmental.
But there are also all the *social* aspects of sexuality (called gender). Who takes care of the children? Who gets paid more? Who does the housework? What do they wear? Do they wear makeup? Shave their legs? Etc, etc, etc. NONE of these is biological. And people can have e range of preferences when it comes to these activities. There is certainly nothing biological that says an XY person with a penis can't enjoy putting on makeup, for example.
So, yes, there is much, much more than a simple binary division when it comes to sex and gender.
Second, the development of sex organs is not an automatic thing based on the chromosomes. It is possible to have a condition known as androgen insensitivity that suppresses the development of male sex organs. This leaves the *default* female sex organs. Often such individuals, who have female external sex organs, do not learn of this condition until puberty (or even later). Again, these are people who are XY and *look* female.
Next, there are the developmental cases of hermaphrodites, where both male and female sex organs are present. often, these cases have surgical 'correction' at birth and are assigned a sex by a doctor.
Next, we have the cases where some more subtle aspect of development is affected and the brain develops characteristics common to one sex while the body develops characteristics of the other sex. It is often the case, for example, in trans-gendered people that the brains show the characteristics of the preferred sex.
All of these are biological, whether genetic or developmental.
But there are also all the *social* aspects of sexuality (called gender). Who takes care of the children? Who gets paid more? Who does the housework? What do they wear? Do they wear makeup? Shave their legs? Etc, etc, etc. NONE of these is biological. And people can have e range of preferences when it comes to these activities. There is certainly nothing biological that says an XY person with a penis can't enjoy putting on makeup, for example.
So, yes, there is much, much more than a simple binary division when it comes to sex and gender.