What's the difference between a moped and a scooter?

It's an historical reference. Years ago (1960s) mopeds were a bicycle which you peddled to get the motor started. They looked more like a bicycle than anything else. At the time the only scooter (at least in the US) was a Vespa, which were very rare. In the American vernacular moped became the common name used for little motorized cycles. Now, scooters are common, but they are often categorized as mopeds because old habits die hard.