I know what you mean about there being two types of ebikes, and agree: one is basically a regular bike with assist, the other is basically a moped or motorcycle. They often look different as well, probably because of the battery size.
The problem I have is that individuals are riding the motorcycle-style ones on paths that are clearly designated as off-limits to motor vehicles for safety reasons. These are paths that see high use, with lots of pedestrians and cyclists, and the speeds that people are riding them strikes me as unsafe. They're often much faster than what someone could physically achieve without a motor. They're also often driven by older children, teenagers, or very young adults, many riding them in pairs, one driving, the other sitting behind.
If you were to step back and just consider the the moped-style ebikes for what they are, that's what they are: electric mopeds or motorcycles on a path designated for pedestrian and cycling use only.
My spouse works in rehab and has started seeing injuries from collisions involving these bikes, and they're basically the same as moped or motorcycle injuries.
I'm not sure what the solution is, because the "regular" ebikes seem just like bikes to me, and it seems strange to require a license and training for them. But it also seems unacceptable to let motorized vehicles on trails specifically meant to be free of them, because of a loophole in regulations.