The videos you posted aren't of caramelized onions, they're sauteed/browned onions. It's a different chemical reaction. You are creating a Maillard reaction of the protein in the onion. Caramelization is a reaction of the sugar in the onion.

I got a buddy who's from Texas, and he makes a mean brisket. He spends like 6 hours on it. I'm from California, and I make a pretty awesome tri-tip. I spend like 1 hour on it. They're both beef. They're both delicious. They look the same if you squint at it right. But they taste absolutely nothing like each other. And that's fine, as long as I don't call my tri-tip brisket and he doesn't call his brisket tri-tip. Cuz they ain't the same thing.