In left socialism / communism, equality among all (often extending to internationalism) and a disfavoring of historic capital / hierarchy are core tenants.

In right socialism / nationalism, specific in-groups are privileged (sometimes a national identity, often even more ethnically-specific) and favoring of (certain, usually sympathetic) historic capital / hierarchy are core tenants.

Granted, realpolitik can muddle these over time. To wit, communist bureaucracy inevitably becoming its own de facto privileged class and national socialism destroying specific capital / hierarchy that opposes it.