Why do some people equate redistribution of wealth with socialism?

Do they not realize that you can also have redistribution of wealth in a capitalist society? Socialism vs. capitalism has to do with who owns the means of production. In a socialist society, the means of production are owned by the populace/government/collective wheras in a capitalist society the means of production are owned by individuals/corporations. Neither has anything to do specifically with the redistribution of wealth. The United States, is, in fact, a mixed economy.