A controller, in the context of remote lighting control systems, is an input device. It can have pushbuttons like a game controller, or have those plus the ability to pre-set some on and off times, or it can be a full-function programming interface that you access from your PC or tablet. You aren’t limited to just one, either. You can use any number of controllers to control the same light.

To work with X-10 remote control devices, the controller must be compatible with the X-10 system.

That essentially means it has to be made by X-10, just as an Atari game system needs an Atari controller