A bicycle with a motor is a Moped. A bicycle with a motor and no pedals is a Motorcycle. Unless I can play music on it without an amplifier it is NOT acoustic ! An "e-bike" serves only for its rider to evade licensing and insurance requirements. So in order to legitimize the so called e-bike, the people with them call them bikes as if they're normal and then have to add a prefix to actual bikes.
The term is used properly for machines that look like a bicycle but have a small motor assist when the rider pedals
ONLY when they pedal
and have a cut off speed of - in this country - 15.5 mph
and the motor is limited to 250W - although how you measure that is something of a problem
and they DO NOT have a throttle
so basically they are like a "normal" bicycle but with a small amount of assistance - but not a lot
and you cannot just sit on them and they go
other countries have different regulations
and some even allow machine with MUCH bigger motors and throttle which, in my opinion, makes them just a motorbike