Capitalism and socialism are not a political systems, but economic theories. Furthermore they are not independent systems but poles of a balance in distribution based respectively on the individual and the common good. All hell breaks lose when we believe we can choose between them, or can steer the ship of state by economic theory alone. This is why I rail against libertarian and capitalist theories when they pose as systems of governance. They are engines without a steering wheel.
Democracy and libertarian ideals are not economic systems but political theories. They two represent poles of a balance between the ideals of equality and freedom respectively. All hell breaks loose when we think we an choose between them, or come to believe that good politics is necessarily good economic policy. They are steering wheels with no engine.
We can argue about the definitions of each of these four elements, but our task is not to choose between them. Our task is to understand what each can and cannot do, and to put all four in balance.