a small contribution;
An engine is always a motor.
But a motor isn't always an engine.
So, this means the term "motor" is a broadest term which appears in many fields. For example, there is a term in the neurology science called somethings like Motor function/disfunction (a kind of epileptic form?) (I guess there is a medicine doctor around here and can confirm this.)
ps: Literally, Engineer/Engineering was derivated from Engine or it has another meaning in English literature? I guess it was derivated from Engine.