Most people, and 3 dictionaries I’ve looked at, use the terms synonymously. However, I seem to recall a technical difference. Anyone?
In general, a motor is something that provides motion or propulsion independent of the energy source. A wound spring connected to a shaft is a motor. An engine is a device that converts potental energy in some confined form (chemical, nuclear, solar, geothermal, et cetera) via a thermodynamic heat cycle using a compressible fluid as the working medium. An engine connected to some kind of shaft or that ejects a propellant in order achieve momentum change is a motor, but not all motors are engines.
In the rocket world, solid propellent rockets are called “motors” and liquid and hybrid propellant rockets are called “engines”. Although the distinction is somewhat arbitrary (as both do work on thermodynamic principles of a compressible fluid that is allowed to expand and cool to extract impulse), solid rocket motors have no moving parts in their main propulsion system (although they may have some kind of thrust vector actuation, deployable nozzles, et cetera) whereas liquid propellant rocket engines and hybrid engines (which have a solid propellant fuel chamber onto which liquid oxidizer is sprayed) have a system of one or more feed pumps (or a pressurized fuel feed system), injector(s), propellant and coolant lines, et cetera. Liquids are therefore mechanically more complicated and have multiple thermodynamic cycles occurring. Solids are mechanically simple (though the design, prediction, and control of solids is at least as complex, and the analytical prediction of the behavior and variance of solid propellant motors in flight is substantially more complicated) and can be modeled as a single thermochemical conversion cycle.
Stranger
Back before the space age, electric motors and internal combustion engines.
And before that steam engines and internal combustion motors.
The only place I have noticed any consistancy on this subject is with radio controlled cars and planes. Electric cars have motors. Gas cars have engines.
In early times, an “engine” could be any mechanical contrivance, like engines of war that were simple catapults and battering rams. IIRC in Gulliver’s Travels, at one point the Lilliputians when itemizing the protagonist’s personal effects, denoted his pocket watch a great “Engine” of unknown purpose.
A motor has always been specific to providing powered movement, I think.
ETA the statement about solid-fuel rocket “motors” and liquid fueled “engines” rings true. The solid fueled rocket has no pumps, tanks, or other mechanical contrivances (more or less), while the liquid fueled rocket has to have at least that.
So, to be strictly correct, the Indianapolis Motor Speedway (which is located in Speedway, Indiana) should be named the Speedway Engine Speedway!
how come a motor boat might have a gasoline engine and it could also have an inboard or outboard motor?
So how come we put motor oil in our engines?
And you may have noticed that we drive on parkways and park on driveways. What’s up with that?
The “gin” in cotton gin was short for engine.
still looking for the gas cap on my engine lathe…:dubious:
As well as Babbage’s analytical engine.
Except for solid fuel rocket motors, I think all motors are engines too.
At least, I can’t think of any exceptions to this, but then I’m not an en-GIN-eer. 
In Soviet Union, engines motor you!
In the vernacular of most Londoners (and possibly the majority of their fellow countrymen) a ‘motor’ is the whole car.
As in ‘Ullo John Got A New Motor’
While not used as such in our every day American vernacular, we’re at least aware of it. “Motor Trend” magazine isn’t about the development of new motors, after all (well, car engines are covered). “Motoring” is something that we may do for fun.
As a mechanical engineer, I’ve always heard the terms used interchangeably…TRM
In older usage I understand “engine” to be synonymous with “device” as we use it now, or “thingamajig” without the connotation of informality or silliness. It is still used in many ways that don’t even imply a mechanical device, like “engine for growth” or “computational engine”. In fact if I remember right, the Gulliver’s Travels section mentioned above also mentions another great engine from his other pocket, which was a comb.
Stranger, I think it’s only accurate to say “engine” implies what you say it does in the specific case of a “heat engine”. Also, there are heat engines that don’t use fluids. Three examples: nitinol belt engines, rubber band engines, and a most amazing thing NASA discovered. For some reason they had a long shaft mounted in bearings at its ends so it could spin, and this was located outdoors, and one day they discovered that it was spinning of its own accord. Well, actually, they soon figured out that sunlight heated the top, making it expand so the shaft bowed upward, and it started to fall over, and never stopped.