Moped is an acronym of two words: "motor" and "pedal." A moped is a motor vehicle with pedals like a bicycle. They were very popular in the late 70s and early 80s in the States because you didn't require a license to ride one, and they got over 100 miles to a gallon of gas. Because they were restricted to 20mph top speeds once gas rationing was ended they quickly lost popularity to traditional scooters and motorcycles.
I remember on steep hills you had to assist the engine by pedaling (that's how underpowered they were). Starting them was fun too... no electric start, you had to pedal like a maniac while engaging the choke and throttle (no electric start). You really couldn't ride them like a bicycle either. Not counting the weight, they were geared so low that even if you pedaled like a hamster on crack you still couldn't make it move as fast as the engine could.
Since our scooters do NOT have pedals, they are not now nor have they EVER been referred to as "Mopeds."