To me, all of those things have something to do with it, but I have a hard time coming up with an absolute definition. The Silverwing, both Burgs, the Majesty, and the BMW are definitely maxi scooters. The BV models, Honda Reflex, Honda Helix, and a few more fall in between. They are loooonng like a maxi, but don't have the displacement. They can be ridden on the freeway, but only at nearly full throttle. Bikes like the SportCity 250, SYM HD200, and other large wheeled scooters are still different from a traditional scoot, like a Vespa LX150, Buddy, Stella, any vintage Vespa, Vino 125, Zuma 125, etc. I call 50cc scooters "mini scoots". And then there is the Honda PCX150. One of a kind. Styled like a maxi scoot, but to small to be one. Can be ridden on some freeways but not others. The former Elite 110 was also in this category I guess. A long stretched out design, but small displacement.
To me the best scooter in the world would probably be the Vespa GTS300 Super. It looks like a traditional scooter, a little bigger but still in proper scale, and fully highway capable. And it is still about the same price as a Majesty (depending on what the dealer feels like adding on to the price)
Used to be the definition of a scooter was simple and obvious. Today about the only differences between a scooter and a motorcycle are where the gas tank and engine are, and a scooter has to be at least partly a step through.