We use “men’s” and “women’s” as a matter of convention. We know there are some men who will fit better in the “women’s” shoe, and vice versa.
The “men’s” style is a bit wider across the toes and in the heel. The women’s, conversely, has a narrower heel and slightly less-wide toe box.
If you’re a man with a very thin foot, or a women with a wide foot, you may want to try the “other” style.