You covered it in your high level list above (which is pretty good) but I wanted to point out Planners as being an important subfield cutting across different applications.
I think those would fall under the first and last point, depending on implementation.
Most so called algorithms taught in universities are after all some form of basic AI, there's very little conceptual difference between an A* planner and a minimax tree, yet one of these is essentially Stockfish, which is "smarter" than all humans when it comes to chess.
