I have two scooters - a Vespa GT200 and a Piaggio BV500. The Vespa can be seen (and read about) here from my homepage.
A good place to get scootering advice and talk is the Modern Vespa Forum, which despite its name is not limited to discussing Vespas, but is primarily focused on “modern” (automatic CVT transmission) scooters, a.k.a. “twist-and-go”.
In general there is a continuum of bike size/engine power from moped => scooter => sportbike/cruiser, but the lines are getting increasingly blurred.
In most states, there is a legal definition of “limited power motorbike” based on engine size or max speed – typically under 50cc, or in NY State, any bike that can’t go faster than 30 MPH. These limited bikes are “mopeds” and cannot go over bridges or on the highways; however, you don’t need a motorcycle license to ride one, just a driver’s license. (You still need to register/plate the vehicle, of course.)
A “scooter” properly refers to a bike that is faster/more powerful than a moped (typically 125-150cc), with smaller wheels relative to a standard motorcycle (10" wheels are standard) and a step-through frame (you sit on top of the engine, rather than straddling it). These are ideally suited motorbikes for dense urban riding, which is why they’re so popular in the narrow streets of cities Italy and France, and comfortable going up to about 50-60 mph (or faster if you’re a small and light rider). Higher speeds than that are not really recommended on 10" wheels, though people regularly speak of taking highways for short stretches on them, and they are highway legal.
“Classic” or “vintage” scooters have a manual transmission with the clutch being a “twister” on the left hand grip, since there is no foot peg like there would be on a motorcycle. Most modern scooters have CVT automatic transissions, though there are still new produced scooters with manual transmissions (the Stella and the throwback Vespa PX150).
Where things get blurry is that a class of “maxi-scooters” are becoming increasingly popular. With larger engines (200cc to even 850cc), larger wheels (12 to 16 inches) and higher top speeds than standard scooters, they are basically step-through, automatic CVT transmission motorcycles that are highway-class.
I did learn to ride a “standard” motorcycle, but since nearly all my riding is done within NYC I much prefer the CVT/auto tranny for the same reason I prefer an auto tranny in my car for city driving: I find dealing with a clutch in city traffic a pain, and even on the highway, I don’t see the romance factor of it. And scooters have underseat storage, which is also nice.
I’m glad to see you don’t equate “scooter” with “not as dangerous as a motorcycle to ride”. While it’s true that the typical scooter will not go faster than 60 MPH, that is more than fast enough to get you seriously hurt, and most motorcycle accidents happen at speeds under 40 MPH and in city riding (the most common scenario being the driver who “didn’t see you” making a left turn from the opposite direction right in front of you in an intersection). The pavement will hurt just as much if you hit it at 30 MPH whether you’re coming off of a Harley or a 50cc Vespa. Wear your gear (full face helmet and gloves are a must).