A few recent posts seem to be mis-identifying scooters as mopeds just because the DMV says they are. Personally, I don't allways believe the government so here goes.
In the beginning was the bicycle.
Then the gearheads of the time said "let there be power assist" and the bicycle became a motorized bicycle, with pedals to start and assist it, no clutch and a belt drive.
Eventually, clutches, gears, kick-starters, chain drive and the like were added and somewhere early in that evolution they were called motorcycles, even though they still had pedals like a bicycle.
With motorcycles fully evolved into a good facsimilie of todays motorcycles, the small ones with bicycle style pedals were called Mo-Peds (there were no big ones with pedals other than antiques, which are more correctly called motorcycles), just as the ones with footboards and small wheels were called scooters.
In good governmental style, different juristictions classified different vehicles as MoPeds for purposes of licensing and registration. Simply put, in some places you can register a Spree as a Moped. This does not the Spree a Moped make.
A MoPed is a Motorized Pedal Cycle. You can pedal it, let the engine push you along or do both at once.
Except for governmental licensing regulations, which do not change the animal, only how you feed it, the above definition describes a MoPed.
Wheel diameter, engine size, transmission type, number of gears... none of these things matter. If it is pedal and/or power it is a MoPed.
I just had to say that. : )