Historically, motor and engine had different meanings. “Motor” was strictly related to movement and the word derives from the Latin: “movere” which is to move. We can see this usage in the modern term “motor neuron” which are neurons related to, you guessed it, movement.
Engine comes from the Latin: “ingenium” which means ability, talent, or character. While those meanings don’t quite make sense initially, they sort of do when you think about how we call medieval warfare devices “siege engines” or the modern term like “game engine.” A siege engine is a device that grants you the ability to siege, a game engine grants you the ability to write games. Historically, things like traps and lures were called engines. Thus, engine was the name for a device that imparts some kind of ability.
Now, coming back to internal combustion “engines” and/or “motors” we can see how something that converts an energy source into motion could both be a motor *or* an engine. It’s a motor because it creates motion. It’s an engine because it’s a device that imparts the ability to move. So, if using the historic origins of the words, an internal combustion device that creates motion is *both* an engine and a motor.
However, if you were to use engine or motor outside of the mechanical engineering realm (say, neurology or game development), motor is about motion and engine is about a device that imparts you with some ability.
EDIT: Sorry if this was ELI10. I forgot which sub I was in. Leaving it though because it answers the question.
EDIT2: I totally forgot more uses of engine that are *not* specifically motor related per se: “search engine”, “engineer”, Babbage’s “Analytical Engine” and “Difference Engine”.
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