When you put it that way… 
Admittedly, in my OP I hadn’t fully thought of the implications. I had assumed that “Categories” was OK, and therefore “Tags” was OK as well. But if “Categories” is confusing, then I don’t have a suggestion.
My hunch is that the “Categories” label is OK. Not all menu items have to be versions of the same thing. They are all different views into the site’s content, it’s just that not all those views are lists of topics. In this case, adding /badges, etc. as I had suggested, is a probably a bad idea.