From t'interweb:
"“Motor” is rooted in the Classical Latin movere, “to move.” It first referred to propulsive force, and later, to the person or device that moved something or caused movement. “As the word came through French into English, it was used in the sense of ‘initiator, A person could be the motor of a plot or a political organization.”
“Engine” is from the Latin ingenium: character, mental powers, talent, intellect, or cleverness. In its journey through French and into English, the word came to mean ingenuity, contrivance, and trick or malice. “In the 15th century, it also referred to a physical device: an instrument of torture, an apparatus for catching game, a net, trap, or decoy,” .
Today, the words are virtually synonymous. “Language evolves to take on new tasks, Without thinking about it, we adapt to new meanings and leave the old behind.” We talk about our car’s dashboard, unaware that in the 1840s, the word referred to the board at the front of a carriage that stopped mud from being splashed on the coachman."
Funny how we now abbreviate "dashboard" to "dash". Isn't language interesting!