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A motion control system is a system that controls the position, velocity, force or pressure of some machine.  As an example, an electromechanical based motion control system consists of a motion controller (the brains of the system), a drive (which takes the low power command signal from the motion controller and converts it into high power current/voltage to the motor), a motor (which converts electrical energy to mechanical energy), a feedback device (which sends signals back to the motion controller to make adjustments until the system produces the desired result), and a mechanical system (including actuators, which physically produce the desired end result).
A motion controller is the primary intelligence, or brain, within a motion control system.  It is responsible for calculating and generating the output commands for a desired motion path or trajectory. Motion controllers vary in complexity; sophisticated motion controllers typically consist of a trajectory generator...