Here is what I found in Microsoft Encarta Encyclopedia:
"Moped, motorized two-wheeled vehicle that is smaller and lighter than a motorcycle. Also referred to as a motorbike or a scooter, the moped is a very economical form of transportation that is popular in Europe, Asia, and many other areas with warm climates and high fuel prices. In the United States, mopeds can be licensed for use on public highways and can also be driven on bike paths in certain areas. Some states allow persons as young as 15 years old to operate a moped with a special driver's license.
The weight, engine size, horsepower rating, and speed of mopeds are limited in most states. A moped typically weighs less than 60 kg (130 lb) and is powered by a small single-cylinder air-cooled gasoline engine (see Internal-Combustion Engine). Moped engines typically have a power output of 3 horsepower or less and are limited to a maximum speed of 48 to 56 km/h (30 to 35 mph).
...Variants of the moped include scooters, motor-assisted bicycles, and minibikes. Scooters tend to be slightly larger and heavier than mopeds. They use larger engines than mopeds and have a flat floorboard and step-through frame for easier mounting and riding. Motor-assisted bicycles are ordinary bicycles with a small add-on electric or gasoline engine that is mounted over wheels. The motor is used only when going up hills or when the rider is tired. Minibikes are small, two-wheeled recreational vehicles designed primarily for off-road use by 10- to 15-year-old riders (although adults sometimes ride these vehicles also). Minibikes may not be licensed for operation on public highways. They are often assembled from kits that include an engine, a simple rectangular frame, front forks, handlebars, and a seat."
I think this is a pretty wide definition.