A person who's "born to rule" belongs to the ruling class, or aristocracy, and is "noble" just by being in the family line — whether they have done anything noble or not. In an aristocracy, a princess who doesn’t visit sick children or clear land mines is still a princess.
"Rule of the best" or "by a privileged class" are 16th-century Latin meanings for aristocracy. There are examples of the "best" coming from ordinary society, no matter who their parents are, but often the aristocracy is made up of families who start ruling and keep the power in the family generation after generation. Kings and queens, princes and princesses, and dukes and earls, are all titles within an aristocracy, though some really hard-working and noble outsiders may earn a spot in the aristocracy too.