Technically they do have both… the starter that starts the engine is a motor. If you have electric power steering, that has a motor. Your windshield wipers have a motor. If you have power seat adjustment, motor. There are many small motors around a car to accomplish things.

Also, personally, I wouldn’t use motor and engine interchangeably. I know it’s very common to do so, but as someone that works on my own vehicles from the time I was 16, they’ve always been referenced distinctly in service manuals. Motors run on electricity, engines run on combustion.