I'm with NASA on this one:
Definitions from their website:
https://www.nasa.gov/audience/foreducators/rocketry/home/rockets_stack_up_nf_prt.htm
Rocket engine -- A machine with moving parts that converts stored propellant into hot gases to produce thrust.
Solid fuel motor -- A simple device that converts stored propellant into hot gases to produce thrust.
Used in a sentance, here is NASA'S definition of the Delta II rocket:
A Delta II rocket has a
rocket engine, two stages, a
solid fuel motor, one interstage, a payload, an aerodynamic nose cap, avionics, a fuel tank and an oxidizer tank. A Delta II rocket does not have a parachute or stabilizing fins.
They've clearly delineated the difference between engine and motor.