Which vibe do you want to ride?

It's a spectrum. A pedal-assist electric bicycle and a Surron are both considered "e-bikes" yet they're wildly different with the other effectively being a motorbike. In europe the vast majority of e-bikes are pedal assist with a 250W motor and maximum speed of 25kph (15mph)

EDIT: Pedal assist (pedelec) means the motor only runs when you're pedaling and usually the harder you pedal the more it assists but it cuts off at 25kph and if you want to go faster it's muscle power only from there on.

I think pedelecs are distinct enough from mopeds to earn the name of e-bike, but throttled variants are a different matter where the line is far less clear.

I agree with you, electric bikes belong on the road.

.... after all cars are banned

I wear a motorcycle helmet on mine