An engine is a motor but a motor is not necessarily an engine.
From American Heritage Dictionary:
1. Something, such as a machine or an engine, that produces or imparts motion.
2. A device that converts any form of energy into mechanical energy, especially an internal-combustion engine or an arrangement of coils and magnets that converts electric current into mechanical power.
3. A motor vehicle, especially an automobile: “It was a night of lovers. All along the highway... motors were parked and dim figures were clasped in revery” (Sinclair Lewis).