Is it an Engine or is it a Motor?

Seems pretty easy to answer until you start your own internal conflict of defining which is which. Looking up the proper definition adds to the dilemma. 
Websters defines a motor as the following and adds engine as a synonym:
mo·tor noun \mō-tər\
A machine that produces motion or power for doing work
1 : one that imparts motion; specifically prime mover
2 : any of various power units that develop energy or impart motion: as

a :  a small compact engine
b :  internal combustion engine; especially :  a gasoline engine 
c :  a rotating machine that transforms electrical energy into mechanical energy  

Looking up engine, resulted in the following definition
and adds motor as a synonym:
noun \en-jən\

1: a machine that changes energy (such as heat from burning fuel) into mechanical motion
2 : the vehicle that pulls a train
3 : something that is used for a particular purpose
4 :  a machine for converting any of various forms of energy into mechanical force and motion; also :  a mechanism or object that serves as an energy source <black holes may be the engines for quasars>

The two would seem interchangeable for the most part. but...

Similarly confusing are lubricants designed to be used with electric motors. First, all of the companies that make these oils call their products "motor oil".  Yet none possess the minimum specifications for use in a lawnmower or automobile engine.
Some of our readers may recall visiting the local hardware store in days past looking for "engine oil". At the time it was the term used to describe a lightweight oil used for a frozen lock, on electric fan or in a sewing machine. In even earlier days, the same was referred to as "machine oil".

Of course there is this iconic warning no one ever wants to see flashing on your dashboard - the "check engine" light... not the "check motor" light. There is irony here too, as the light can be triggered by any of dozens of issues, many which have little to do with actual engine operation. Further when describing the electric power plant used in EV's, they are called "motors"
The term "engine" has also crept into terms used to describe various computer hardware and software, yet there are no moving parts, nor do they convert power into motion.

The School of Engineering says, "The Oxford English Dictionary defines “motor” as a machine that supplies motive power for a vehicle or other device with moving parts. Similarly, it tells us that an engine is a machine with moving parts that converts power into motion." That would indicate full interchangeability. But are the words virtually synonymous? Not really. 

I are not a "Steam Motor"
Despite the supposed interchangeability of the two words, when compared side by side, the results sometimes depict synonymous terms, other times odd, maybe questionable use.
General Motors vs. General Engines
Ford Motor Company vs. Ford Engine Company
 Radial Engine vs. Radial Motor
Race Engine vs. Race Motor
Lawn Mower Engine vs Lawn Mower Motor
Wiper Motor vs. Wiper Engine
 Rotary Engine vs. Rotary Motor
Outboard Engine vs. Outboard Motor
Rocket Engine vs Rocket Motor
Search Engine vs Search Motor
Steam Engine vs. Steam Motor
Jet Engine vs. Jet Motor
MoPar vs. EnPar
BMW vs. BEW 
Engine Rebuilder vs. Motor Rebuilder
Engine Hoist vs. Motor Hoist
Engine Stand vs. Motor Stand
Engine Coolant vs. Motor Coolant
NginX vs MotrX
Game Engine vs. Game Motor
Graphics Engine vs. Graphics Motor
Engine Torque/HP vs Motor Torque/HP 
ECU (Engine Control Unit) vs. MCU

Why not have some fun and challenge your coworkers to define which is more correct? Let us know if you come up with additional terms (such as those above) that we missed. Use the comments below to sound off.