Right wing politics is more about enforcing social hierarchies and capitalism, which teeechnically conservatism doesn't have to be about. Of course modern western conservatism is largely regressive which directly means it's trying to re-enforce older harmful social hierarchies. Hence why stuff like liberalism still ends up on a right-wing spectrum, as it's a big defender of capitalism and social hierarchy in practice, even if liberals often think of themselfes as being socially progressive in theory.

Abrahamic religions of course are largely inherently right wing in execution. It's hard to find any western religion that doesn't believe in and preaches the value of social hierarchies and worships some form of capitalism.

Right wing politics and conservatism are more homeostatic rather than intrinsically the same, so to say.

Just additional info on exact definitions, not disagreeing with you.