Re: who has a moped license?
In the USA, different states have different laws about mopeds, what riding one takes, and what qualifies as one.
Back during the 1970's when the moped craze peaked (during the manufactured "oil crisis" in the USA) most states de-classified mopeds from motorcycles. You did not need any specific motorcycle license for them; as long as you held any type of valid drivers' license you could operate a moped.
I was told that there is a general move towards eliminating the moped classification at the state level, and just requiring the same motorcycle license for anything with less than four wheels. I'm not real sure of what the reasoning for this would be, because mopeds aren't normally operated with regular traffic anyway. Maybe the people at the drivers license place were losing business and needed something else to take up their time?