Like most mopeds, they were 2 stroke. The exception was the Indian, which was 4 stroke. I had a 1978 Honda Hobbit. Ohio, and a few other states, had an odd law that mopeds could not go more than 20 mph. My Hobbit was the red model, but some other states had the yellow model that could scream at 30+ mph.
A friend of mine had a Puch. It seemed pretty no-nonsense. It was more stripped down than mine, and could go 30 mph. Another brand at the time was the Sachs.
They were nice for a kid that was under 16 years old and wanted something faster than a bicycle. After I turned 16 and could drive a car or motorcycle, I had no desire to ride my moped.
When I first got my moped, I was one of the first kids in town to have one. Later on, they really caught on. A lot of kids had them. State law only required you be at least 14 and have an operator's license for a moped. After more and more kids got them, then they changed the law and you had to get plates for them and had to wear a helmet. That KILLED the moped market.
I guess if you want something thrifty on gas that you can just ride around town, they are OK. The other thing is the pedals on the moped were only good for starting it. You would put the moped up on its stand which took the back wheel off the ground, turn on the ignition, turn on the gas petcock, and then start peddling. The gearing was so low that it was extremely impractical to pedal it like a bicycle without the motor. If I were ever out and ran out of gas, it was easier to push it home than try to pedal it.