This is an excellent compendium of moped definitions, but the most useful one is the state definition. I realize that statement may rub against the grain of a generally anti-authority cult here (and I consider myself among them), but all the other definitions are just semantics. The only definition that should affect one's behavior and decision-making is the legal one. I have been considering upgrading from my 50cc moped to an 80cc scooter, for safety reasons, mainly, and the law in Michigan says that I would need to then get a motorcycle license because the engine has more than 49.9 cubic centimeters. That's the only definitional difference between the two machines that matters to me. The other variances, e.g., pedals vs. no-pedals, floorboard vs. no floorboard, are all potentially important personal preferences, but I don't really care what you call one vs. the other.
If one decides to increase to increase the displacement of a "moped" to more than 49.9 cc's with a speed kit, he or she can make a personal decision as to whether or not to register the machine as a motorcycle. But the decision should be made knowing that, technically, the moped is now a motorcycle according to the State. If I choose to flaunt the law (which I may very well do --- a speed kit is another of the possibilities I'm considering and I don't intend to go running to the Secretary of State's office with a press release about it) then at least I'll know that I'm in technical violation, which could, theoretically, earn me a fine. THAT is the only definitional difference that really matters, isn't it?