A DCC term for the controller used to operate a train. It has the throttle, plus other controls needed.
A Cab is the (typically handheld) device that is used to control a train. The user has controls for speed and direction, and a few other functions. More sophisticated cabs have more buttons for more features such as sound. CAB is the correct NMRA definition for the control device. The term is derived from the fact that the operator has all the controls the engineer has in the cab.
Cab Control is an old analog method, which usually involved a lot of electrical wiring and switches to connect the cab to the train the user was controlling.