Actually, most scooters have modern 4-stroke engines that are much more similar to motorcycle engines than old moped engines. In fact, the newest models have electronic fuel injection and engine computers just like cars do.
I'm aware of what vespa means in Italian.
It actually got its name more from the shape of the rear end on the original 1946 prototype than from the sound it made.
But yes, it is an common mistake to make for the uninitiated, which is why we scooterists are quick to correct it.