>> Today, the words are virtually synonymous.

Ehhh that's a stretch, unless we're talking Real Housewives type of "lay people".

As I understand it (within an engineering context), a "motor" converts electrical energy to mechanical energy, and an "engine" takes thermal/chemical/some other form of mechanical energy and outputs mechanical energy. But it's confusing because I've changed the "motor" in my old Honda when I was a teenager. So while I agree there is some nuance and blurry lines, not sure the two words are quite "interchangeable".