People that are left wing support capitalism. People that are right wing support fascism.
Socialism is the belief that the government should be responsible for ensuring that the people are fed, clothed, housed, educated and healthy using the taxes they've collected. Socialism can only work when built on a capitalist framework that provides the economic growth and prosperity that governments can tax to provide necessary services. If you have a national health service, livable safety net social support services, you're in a socialist country.
Fascism is the belief that the government can use the people as cannon fodder in forever wars and all taxes collected are to further the enrichment of the oligarchy. Capitalism, ownership by many, is replaced by an an oligarchy where all wealth is concentrated in the hands of a few who are entirely beholding to the state to provide their military and civilian protection. By keeping the population sick, poor and hungry, it makes them easier to control. Inadequate healthcare, high energy costs, and the only work available is join the army and go die in a forever war is a sure sign you're living in a fascist society.
Communism and fuedalism are the same, the state/king owns everything including the peasants.