"What about old old money? I'm talking about people that have money because their ancestors were royalty of some sort."They would fall under the rubric of what the parent comment said about "rose to political power." The old nobility got that way because they supported the king in military campaigns in exchange for titles, land, and protected agricultural or mercantile monopolies and warrants. (Incidentally, the origin of the word "entitled" dates back to the titling of the nobility by royal authority. A title is, in essence, the exclusive right to something. In many cases, that right was to specific regions or lands. When we say that someone is "entitled to" something, or "has a sense of entitlement," we are figuratively harkening back to an age when an "entitlement" was something very literal.)
For what it's worth, the fluidity of the nobility is vastly underreported in popular conception. Noble families rose, fell, were made, were broken, etc., about as often as in Game of Thrones. Today's "old old money" descends from the old old noble houses who, by some combination of luck and savvy, ended up on the right side of countless civil wars, uprisings, wars of succession, and dynastic transitions.
Did these families "earn" their fortunes? I'd say no more and no less than any of today's political elites. We're kidding ourselves if we believe the political patronage system in the US is all that different from the political patronage system of the Tudor dynasty, or that of Louis XIV. The mechanics of government are different; the rules of the "Game" are entirely unchanged. (Replace "King" with "Presidential Administration.")