A pedal-assist e-bike with a 500 Watt motor and an easily bypassed speed governor looks like a bicycle, it is pedaled like a bicycle, and yet it is unsuitable for a bicycle lane or a path shared with pedestrians.
Pedal-assist feels to me like a complete red herring to the actual issues. It's often an arbitrary line but it doesn't make much difference to safety at all. (nor, IMO, do power limits, because it either limits cargo bikes or makes lighter bikes a lot less predictable: I would think an acceleration limit would be a more sensible option).
(build-in speed limits that are significantly below what the average cyclist can achieve by pedaling also seem kind of silly. IMO people might not bypass such limits as much if the limit was put at a more sensible level)
They are popular for cargo bikes; picture a parent with a couple of kids, or a big grocery run. They are also a great way of commuting without having to worry about being sweaty when you arrive, if you have a long commute. Lastly, they are great for people who are getting back in shape or starting to suffer the effects of aging. They are great all around.
Not really. The first motorbikes were bicycles with engines attached. Many current electric motorcycles are bicycles with electric motors attached.
If it has a throttle and does not require pedal assist, it is a motorcycle.