The registration with DMV and a license for special vehicles is not required for driving on a motorized scooter. However, you will need regular driving permits.
To legally operate mopeds, moped riders require an official motorcycle license, that is registered with their moped as well as the appropriate license plate.
A motor that is electric (less than 775 Watts) as well as pedals constitute the primary conditions to determine if the vehicle can be classified as a bicycle that is motorized in California.