Cars have engines (the ones with Diesel or Otto engines, that is) Only the electric ones have MOTORS...yet...
You register your car at the Dept of MOTOR Vehicles. You MOTOR about in your car, on MOTORways. It might have been made by Ford MOTOR Company or General MOTORS. You are called a MOTORist. Mr. Toad had a MOTORcar.
I drive a 1978 Honda CB750K MOTORcycle, that has, the last time I checked, an engine.
The person in charge of a fire department, that has ENGINES and TRUCKS (not the same thing, at all) are called, officially, Chief ENGINeers, or "Chief" for short.
The person who controls the subway train is a MOTORman, unless you read the newspapers, and then (s)he is a "Conductor."
Truck (US) = lorry (UK) Semi (US) = artic (UK). Sem'-EYE (US) = Sem'-EEE (Canada)
Trains are made up of cars, which ride on trucks. Sometimes trucks and cars ride on rail cars. WHISTLE posts (with the big "W" painted on them) tell the engineer when to blow the HORN.
A coach became known as a "bus" which is short for "omnibus" which means "everybody" which meant that any person could board and get a cheap ride, even the ones who couldn't afford to ride in a coach.
A taxicab is short for "taximeter cabriolet" which has a (meter) inside a hired (cabriolet) that adds up the fare (tax) to be paid by the passenger.
There's a couple of passenger cars in my driveway, and quite a few passenger cars in my train room.
(With a nod to George Carlin)