Disinterested Third Party
Funning thing, that the "engine" is attached to the aircraft with "motor mounts," isn't it? There was a time when we were rated for Engine and Airframe, and were called "A&E's." Today the FAA refers to it as Airframe and Powerplant, and we're sometimes called "A&P's."
I'm one of those powerplant mechanics, and most of us tend to refer to it as an engine, motor, pratt, garrett, lycoming, continental, #%@* of ^!#%*, and a few other terms.
I just performed a compressor wash on an engine a few days ago. We motored it while pumping fluid in through a hose.
Engineers get caught up in the differences between motors and engines. Most of us who actually get our hands dirty would prefer that engineers stay as far away as possible, lest they get hurt. It's better for everyone.
From a pilot perspective, I use the terms interchangeably when referring to the powerplant, and refer to blower motors and and the link by the name most likely to identify them to the person to whom I'm speaking. That's seldom "engine."