An electric bike is really just a bicycle with an electric helper motor tacked on. Some places limit the weight to around 35-40 kgs and power to 250-750w with a 15-20 mph motor cut off speed depending. You can pedal along meaningfully as they're going bicycle speeds, and really should if you want to go somewhere any faster then 20mph, or if you want to go far. Most all of them need some pedalling to go uphill even given full throttle. Also, they end up looking mostly like bicycles. If it looks like a duck, quacks like a duck...

Mopeds are built as lightweight motorcycles, they've got motorcycle tires with terrible rolling resistance, heavy weight, a motor that makes it go around 30mph and symbolic pedals tacked on. Symbolic partly because of the weight and rolling resistance, but compounded because they're geared unusably low and you can't really use them due to the position, or if you managed to you'd end up hurting your knees and such. In effect they're really just used to make it legal as a moped, although some need to be started by pedaling from a corner. They tend to look somewhat odd, or I'm not used to them, but they definitely don't look like bicycles.

The next category up is LSM (limited speed motorcycle) something like a scooter falls into this category, limited to around 70km/h. Beyond that you're riding a full blown motorcycle.

BTW, I know a guy who got a criminal citation riding a two wheeler he described as being an "ebike", even though it did not correspond to such... Guess that's something to think of for people who like to call their motorcycles "ebike" despite it going >40mph on it's own power for example... Call it what you will, but that's not an ebike...