I would say that categories are the general classification of an article, while tags are a grab-bag of ephemeral keywords that people might search through. Sections, on the other hand, are a there-can-be-only-one organizational tool that affects the URL and determines things like which RSS feed an article appears in.
So, for instance, /reviews is a section, “Doctor Who” is a category, and “season 10”, “spoilers”, and “plot holes” are tags. An article in a separate section called /fanart could be in both the “Doctor Who” and “My Little Pony” categories, tagged “bill potts” and “twilight sparkle”.
You might not need all three, but they can be used to organize a large site. Personally, when I migrated thousands of entries over from MovableType, I made each blog a section, made a 1:1 mapping of the old categories from the primary blog to Hugo categories, and was surprised to discover that I had actually used tags for the first several years, until I got tired of typing them in.
Since I added Xapian Omega as a search back-end a few days ago, I don’t see any reason to re-tag the old posts and start tagging new ones by hand. Broad categories are sufficient for organizing articles, and anyone who wants to find out what I think of Peter Capaldi as Doctor Who can just hit the search button in the navbar. That’s generally more useful than manual tagging.
-j