Values & Goals
Leftists advocate egalitarianism. Socialists want greater material equality so as to reduce socioeconomic stratification. Radicals tend toward pure democracy. Rousseau, the founder of modern radicalism, demanded equity in political power, as did Marx. Liberals are more milquetoast: accepting representative government while insisting that political power ultimately be in the hands of citizenry.
In contrast, the right are unabashedly elitist. Social stratification is natural. To conservatives, capitalism serves a societal function in separating winners from losers: from those deserving esteem and those deserving less in every way. It salves the conservative conscience that capitalism is the status quo, and so may also be revered as conventional.
While capitalism is today a conservative institution, it started out as a liberal challenge by Adam Smith to the mercantilist status quo. Smith was wildly optimistic in thinking that social stratification was not natural, as egalitarian societies have been largely absent throughout human history.
Marx asserted that nations were artificial boundaries designed by capitalists to divide humanity and distract them from their commonalities. The left generally value the spirit of fraternity, and tend toward internationalism. In contrast, those on the right are prone to be patriots.