We interchange the word engine and motor a lot. There is a song called Damn this Traffic Jam and one of the lyrics is: "it hurts my motor to go so slow." Exxon- Humble Oil Company had a slogan with a guy waving- his head was a drop of oil. their slogan was "Happy Motoring". So there is evidently quite a gray area here: when a major oil company calls the engine a motor, makes it their slogan, and no one catches it! I worked for MTU for about 18 months. My first language was German, so I found myself surrounded by a bunch of homesick Master Mechanics who called upon all entities when they swore- they took cursing to the next level!- and who referred to Diesel engines as "motoren". Maybe there is something lost in translation, I dunno.
So, what is the difference between an engine and a motor?
Motors are electric. Electricity powers motors.
Engines are powered by come sort of pressure or combustion, ie: steam engines, automobile engines, diesel engines.
Pretty simple, really.