I think of it like Kingdom, Phylum, Class, etc from biology class.
Music is Kingdom. Genre Category is Phylum. Genre is Class. As hiccup said above, Genre Categories have multiple included Genres, which is what makes them categories, but Genres can belong to only one Genre Category because they're specific.
Another way to think of it is that Genre Category is really the Genre, while what we normally refer to as Genre is actually more a description of style(s).
I struggled with genres a lot when I tried to get really cute with descriptions and subtle differences in genre. Categories help break you of that when you realize that everything really does fall somewhere under those big umbrellas.
A smile is happiness you'll find right under your nose.