Social dominance orientation and right-wing authoritarianism are distinct personality syndromes despite shared prejudice.

Evidence

High SDOs also resemble High RWAs in being politically conservative. … Their similarities in prejudice and political conservatism aside, however, you can see from Table 4.1 that social dominators and right-wing authoritarians hardly resemble peas in a pod. Most notably, high SDOs are not particularly religious, but high RWAs usually are. Similarly, high scorers on the SDO scale do not claim to be benevolent, but high RWAs do. In contrast, social dominators have a wisp of hedonism about them, but authoritarians disavow such. The former do not need structure nor value conformity and traditions, but the latter do. Social dominators tend to be men; right-wing authoritarians do not. And quite strikingly, high SDOs do not see the world being nearly as dangerous as authoritarians do, nor do they appear to be nearly as self-righteous—implying their prejudice does not have the same psychological roots that previous studies have unearthed in right-wing authoritarians. — John T. Jost and Jim Sidanius, Political Psychology, 961