Here in France, the law is pretty clear : if it has 2 or 3 wheels and is propelled by the rider, then it's a bicycle. Trikes are bicycles too. There are a few extras : 2 mandatory brakes, lights if it's dark, reflectors, that kind of stuff.
As for e-bikes, the limit is 250W, 25 km/h, and the motor must only run if you pedal. In this case, legally it's a bike. Above that, it's a moped.
As far as I'm concerned, if I can pedal the thing (without motor) to the local equivalent of Home Depot and come back with 2x 10 kg bags of mortar in less than 1h30, then it's a bike. Of course, the store is 15km away on the other side of a 400m high hill, so this puts some conditions, which seem to exclude Dutch 3-speed "urban" bikes
, and also anything that can't corner at 60 km/h downhill with a load of stuff on the rack, like upright trikes, etc.
The 250W limit (decided by the idiots in power in Brussels) has an interesting consequence, it turns all hub motor ebikes into Dutch e-bikes unable to climb any kind of (even wimpy) hill, cause the motor isn't powerful enough to run 25kph uphill, so you'll go 10 kph, efficiency drops from 80 to 30%, and it overheats then stalls, then you got to leg it. I thought the motor was supposed to help specifically uphill... but no, those only work on the flats. To get over serious hills, a 1500W hub motor is needed so it can always stay at its optimum speed and efficiency (unless the rider is very fat or carries lots of heavy stuff, in which case you need more).
So here if you want an e-bike that can actually climb (which is the point IMHO) you need a crank motor which will cost about €1000 more. Since this motor uses the gears it will work at optimum efficiency even at 10kph and will get over that mountain without burning.
I'd like to get an ebike (or a propane bike) for commuting to the city, cause some days I don't feel like sweating. But for me it would have to bring some advantages, namely make it faster to climb the 10-15% (and especially the little bit at more than 15%) slopes on the way. I'd have to pay 2000€ for that, and that's a bit stiff. I'd much rather add a Cyclone motor to my current bike, but the idiots made kits illegal too !