alt Hacker NewsA party can be socialist without being Marxist/communist. It’s an older understanding of “left” and the current split between left and right has become a cartoon. But one could say that during the Second World War the Germans and the Russians were fighting in part over a radically different ideological approach to implementing a similar socialist system.
It's been dissected ad nauseam, but at base they're drastically different arrangements of who and what structures are privileged.
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.