A controller can be defined as any device that connects to lights and makes them operate. Just because it involves the Pi does not mean that it is not a controller.
Generally people refer to 'controllers' as devices that have an onboard computer/processor that manages the data from some source to operate the connected lights. The Pi and Pi hat is just a miniature controller and even if you are true hacker and hook up the lights directly from the expansion connector it is still functioning as a controller.
A rose by any other color is still a rose.
