Not quite - in a very classical form of Conservatism, the Monarch and Nobles would have a different set of laws and social conventions. Usually, it's not an ideolgoical thing.
Aka Magna Carta '3 tiers of society' - the Monarch, Nobles, Plebes etc.
Or in Roman society, Nobles/Senators, Free people, slaves.
How is this different from what I’m saying? What you listed is precisely the examples of what I’m talking about