To add to the ambiguity, rocket powerplants are also called both "rocket engines" and "rocket motors" and the terms seem to be somewhat interchangable.
Having no books handy at the moment, I will say, based on my subjective impressions of lots of personal stuff (and also Larry Clark's book "IGNITION!"), the breakdown is:
Politicians, program managers, Pentagon brass, defense CEO's, and some pretentious ******* celebrity scientists like J. Robert Oppenheimer: ENGINE people
Real scientists, engineers, metallurgists, machinists, hazmat teams, NCO's, and anybody near a test stand when one blew up: MOTOR people
There are of course exceptions to this keenly observed rule that I just made up.
Overall in English the word "engine" can mean something much bigger than the word "motor":
- Ships and spacecraft have engines.
- It can mean economic cause and effect ("But well Bob, the numbers clearly show that totally wack-ass accounting one-offs were the actual engine of Uber's so-called "profit" this quarter.)
- You might hear the underground thrumming of "vast, mysterious, ceaseless engines..."
- (You might also be crazy, too. But you would still likely use "engine", because you read it in a book or somewhere and it sounds bigger and more scary.)
- Etc.
But if you just bought a police car at auction most people would say, "It's got a cop motor, cop tires...."
In conclusion, engines are big, motors are more personal and can even be inside of you, also (allegedly) Beer's great, God's good, people are crazy, and even weak imitations of Jimmy Buffet are better than recent Bro-Country.
BR