Вот вариант еврозоны:
The drivers license category for mopeds across the E.U. now is the AM driver's license. This license is for scooters and mopeds with no more than 50 cc (3.1 cu in), and a maximum speed of 45 km/h (28 mph). E.U. member countries that had not fully implemented the E.U. directive that refers to the moped and other drivers license categories had to do so by 2013 at the latest.
The "E.U. moped" is a scooter, moped (or similar) with two, three or four wheels, a maximum speed of 45 km/h (28 mph) and an obligatory license plate as proof of insurance. Many E.U. countries only require special insurer issued plates, not state issued plates.

А вот конкретно для Германии:
German law has two categories for mopeds. The first and slower category is the so-called Mofa, with a maximum design speed of no more than 25 km/h (16 mph) and only the driver is allowed on the bike, no passenger. Minimum age is 15 and no license is required, but a written test has to be completed.
The second category is the Moped, with a maximum design speed of 45 km/h (28 mph), minimum age is 16, a drivers license is required, one passenger is allowed if the moped or scooter is certified for a passenger.

Both types need an insurer issued license plate, which is much smaller than regular state issued plates, which have to be renewed every 12 months, changing the color of the plates every year. Since a 16-year-old can now drive a 125 cc (7.6 cu in) bike, and scooters in the "moped" category allow for transporting a passenger comfortably, mopeds, even though they have less power, more appeal, and space, have almost disappeared as a result of the new E.U. laws. Most teens that don't have the money for the costly A1 driver's license (1st step towards the full motorcycle license), which allows them to drive a 125 cc (7.6 cu in) scooter or motorcycle, go for the less expensive AM driver's license, which allows them to drive a moped or scooter with a maximum speed of 45 km/h (28 mph), but less than 1% chose a moped over a scooter based bike. Modern scooter design and amenities have effectively changed how teens chose their first set of wheels in Germany.

Категорию А они тоже считают мопедом, но правовой статус как у велосидеда.