Topic on Glossary talk:Controller
Controller Mate seems to be a usual mouse/keyboard to controller program. I have already moved the Xbox 360 Controller driver to the controller's page.
There probably isn't much to say about HOTAS beyond the limitations that were previously described in the multiple controllers section (which would also apply to other situations like mixing wheels and pedals). A HOTAS controller has standard controller inputs (buttons, axes, hat switches) so will function as expected (there are even some XInput models).