The difference between sautéed and caramelized onions is that caramelized onions have been cooked long enough that their natural sugars are coaxed out and everything starts to turn deeply golden brown and jammy. As you continue cooking them, some onions will start to break down, the color will be darker in spots, and you'll start to notice fond (spots of caramelized sugar and onion) on the bottom of the pan. You're done once you get to the point where there's not much moisture left and you've got a pile of deep brown, jammy onions—at least 30 minutes. Taste one to see, your onions should be sweet and velvety soft.