What I can do with a category is present a fixed set of classification tags to the content creator, with no risk of spelling ambiguities.
Per group or place, which is another important distinction, I think - tags go beyond any given space while categories are structured per space. I agree that they could be more aligned - and of course would like a category widget (I followed this thread from that one).
The other thing you can do with tags but not categories is filter a search - though apparently you could ten years ago... this would also resolve the widget problem as you could save the content of the search for an RSS widget, but I'm guessing is part of the reason there's no widget for category in the first place? Categories at this point have become more or less useless for us.