I mean, “rich kids” itself is kind of just an extension of what they are allowed to have, and what is officially considered their possesions. I think biological vs step is a meaningless extension. Say you are one of Elon Musks huge wave of kids, you are as rich as whatever payoffs he gave the mother, provided the mother actually spends it on you. Or one of the russian hookers or whatever the heck gates was up to you may very well be poor as hell.

You can have rich parents that you stay with, but they spend less on you than your average barely making ends meet family.