e-bikes are basically electric versions of the old autocycles - pedalling is the primary drive method but they come with motor assistance. mopeds are esentially the other way round and haven't even been required in the UK to have pedals for a while now.
I think mopeds used to be limited to 4kW but now seem to be limited by speed (45kph). E-bikes are limited to 250W and the motor cannot assist beyond 15.5mph (about 20kph) (
source). So they have different primary drive, power and top speed, which makes me think the line is somewhere between.
So you keep claiming. I think that's probably junk and it's just as well I also know groups where they're welcomed.