There are cars powered by gasoline, and they have engines. Then there are cars powered by electricity, and they have motors. A hybrid car, of course, has both a gas engine and an electric motor. The difference can’t just have to do with the fuel, because if you have a small boat, you can attach an outboard motor that’s powered by liquid fuel, unless it’s an electric outboard, which is also called a motor. If you have a big ship, it probably has a diesel engine that’s also powered by liquid fuel. Rockets can be powered by either solid or liquid fuel, and those are called rocket engines — except that they’re also sometimes called rocket motors. In fancy showrooms expensive autos are sometimes called “motorcars” (on the assumption that longer words mean a higher price), but then they’ll open the hood to show you… the engine.
The technical definitions of “engine” and “motor” try to point out that they are actually two different things. An “engine,” this explanation claims, either contains its own fuel or is part of an integrated system that contains the fuel. A “motor,” on the other hand, gets its fuel (or energy) from outside itself. This is clearly nonsense; an electric car contains a contraption that turns the wheels and another contraption that supplies it energy, which is carried along with the car. But we don’t call it an “electric engine” just because it’s in a car, while the fan you plug into the wall at home has an “electric motor.” Same problem with an outboard motor on a boat; they all have fuel tanks, and on the little ones the fuel tank is built right into the top of the thing itself. You can’t get a much more “integrated system” than that, but nobody calls them “outboard engines.” Unless they’re attached to airplanes, in which case “outboard engine” is exactly what we call the power units mounted outermost on the wings.
English borrowed the word “engine” from French sometime in the 1300s, and for quite a while it didn’t have the slightest thing to do with machines. Although to be fair, not much in the 1300s had anything to do with machines. Anyway, “engine” originally meant a person’s ingenuity (one guess where that word came from) or cleverness. It was used in a way that we don’t recognize at all: “Tho wommen were of great engyn.” There was also “false engine”, which meant ill intention, and even spawned its own word, “malengine.” In an odd sideline, in the late 1500s “malengine” became “male engine” — it still meant bad intentions, so you can make of that what you will.
Another way “engine” was used early on was to mean the product of someone’s clever thought. “Nor did he scape By all his Engins,” is the way Milton put it in Paradise Lost in 1667. It’s probably from that sense of “engine” that it came to mean a device of some sort — and I suppose it’s no surprise that the first kind of devices ever called “engines” were machines for torture, most especially the rack: “Have you so us’d confession as an engine To twist and torture silence to your purpose?” (1784). From there, the word was available to be applied to more and more complex contraptions as they were invented. But the key is that “engine” at first meant nothing more than an idea and what might come of it, whether it’s a machine or not.
“Motor,” on the other hand, has always meant something that provided motion. It might have been a person or an animal before there was such a machine. Note the similarity between “motor” and “motion;” it’s not a coincidence. “Motor” was also borrowed from French, but about a century later than “engine.” Just like “engine,” though, it was at first more likely to be applied to people than anything else. The leader of a group or movement was called its motor: “Bagnall that was prime motor in the counties of Katarlagh and Kilkeny.”
As soon as any sort of machine was invented that could impart movement, they were called “motors:” “Whose prime moter or spring..being set true,..the outward wheeles, motions and indications cannot go amisse.” That’s from the 1600s, when clockwork mechanisms started to become relatively commonplace.
The current situation, where “motor” and “engine” are used pretty much the same way, came about around the late 1800s when the idea arose that if something moved, it was probably mechanical. By now we’ve absorbed that notion so deeply that it’s hard to think otherwise. In those days, the most common motive power was a steam engine (in a railroad locomotive), which clearly carried its fuel (wood or coal) and obviously consumed it, sending out clouds of toxic smoke. When electric motors started showing up in the 1800s, although they consumed energy too, it wasn’t at all obvious how. Electricity was quite the mystery to most people in those days. Unlike today, of course, where practically everybody can wire up a three-phase motor control circuit during a commercial break.
In any case, the distinction between motors and engines is now nearly erased, at least in common usage. And I’m not sure anybody would be motivated, even remotely, to try to engineer a reversal.