The difference is that social democrats do not favor nationalization of the means of production, but only a vigorous welfare state. The economy would remain mostly in private hands.
Most countries in Europe are social democracies – and by now, that seems to work better than anything else that has been tried – better than Communism, better than the American version of capitalism.
Americans, I know, are vague on the difference – I just watched a documentary which repeatedly called Hugo Chavez a Communist.