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The down and dirty answers...
Laws vary by state for licensing and registration of mopeds/scooters.
Some states require a motorcycle license, tag and insurance for any motor driven bike or three wheeler ridden on public roads.
Most scooters and mopeds are lettered as 50cc but are usually about 49.6 cubic centimeters in actual displacement. This is the design of the GY6 engine used on many of the Chinese imported scooters in the US today.
They are referred to as "49cc" mopeds usually by people wanting everyone to be aware that they are "street legal" without a tag.
As you can see in the Georgia Code, any Scooter / Moped 50cc or below is included in the same category.
"Licensing" in the above link refers to licensing of the "vehicle", not the person riding the vehicle.