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Motor and engine are generally used to reference the same object or type of objects.

Neither is a direct reference to the fuel used in production of power, nor the type of energy output.

However, in literal terms, anything which provides motive force by transference of energy should be referred to as a motor. An engine is a device or object which converts something into something else, hence Google and their search mot... engine.

A cigarette lighter might be described as an engine, because it converts the input of fuel, spark, and surrounding air into heat and light. It would be a light and heat engine.