"Engine" essentially means "contraption", a mechanical assembly
to carry out some complicated "works".
Weaving engines, threshing engines, analytical engines,
calculating engines, lifting engines, etc. Probably someone
in 1750 made a pun about a lifting engine lifting an engine.
It's an old word.
Motor at least has a root involving "motive" as in motion as
in auto-motive, self-moving. And so on.
I bet it's a new word.
If people know what you're talking about, it's the right word.
"Boat anchor" sometimes works :-)
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