The control can be done at the signal level, you will always need to couple these signals to a circuit in charge of handling the power. Then if it is a remote control I guess we are talking about a wireless one for which you will have to adapt an extra module for communication that can be bluetooth, wifi or RF.

The function of these devices is to manage the control of the outputs based on values in the inputs, this is done by the code that we program. However a complete control is always composed of sensors, controllers and actuators. The Arduino only represents a part of the system which is the control.