Then again, language use is inherently 'sloppy': ultimately, there simply is no one authority that could decide on the exact meaning of the terms we use. What I mean with
gender is not exactly what you mean with the same word, which again is not exactly what you'd see in the Oxford English Dictionary, and so on. One of the interesting things about language is that despite this lack of formal definition it still is useful for communication, and there's a large amount of research literature in several fields on just how it all works.
The way I see it the problem isn't just in the distinction (or lack thereof) between
sex and
gender. The real problem is that while there are real differences in anatomy, behaviour and social roles, the way we distill those differences into concepts is a generalisation of what's going on in the real world. Yes, we need to generalise and simplify things, but that also means that the whole truth is always more complex than our verbal description of it. Our use of languages forces us to see things in an either-or fashion.
(Sorry, this is getting a bit too abstract even for my tastes.

)
Anyway, the bottom line is that
male and
female are words. Ultimately, they are idealised combinations of sex/gender traits, with an artificially sharp border around the prototypical male or female. Just exactly what that prototype looks like is ever so slightly different with each of us, and similarly the exact shape of that border is different. Most of the people I'd call male are people you'd consider male as well, but there are individuals whose sex or gender falls so close to the borders that it's difficult to decide, even if we know exactly the relevant anatomical and behavioral details.
Okay, that's answer number one. Answer number two is that gender -- that is, the social and behavioral part -- is to a large extent based on various properties that are tied to the physical body (including the neurological aspects of the brain). In other words, it is not entirely a social construct. On the other hand, there's also a very large amount of gender expectations that really have nothing to do with the physical sex but are instead something the society has developed at some point over the past couple thousand years. So, yes, it's a social construct, but still one grounded in physical sex.
Nfr