Viewing it entirely in economics is incorrect. All of the above can be done under capitalism. The key difference is not what form of economics are employed but which class controls power and puts the resources of the state to use.

The capitalist state is a state where capital owners hold power and use that power to exploit more capital.

The socialist state is a transitionary state in which the workers have seized power and use the state to repress the bourgeoisie and put resources to their own use.

The communist state is what occurs when capitalism is entirely defeated, all nations are socialist, conflict is eliminated and material abundance is achieved, at which point states start to stop existing as the resources within them that are put towards repressing the bourgeoisie through violence are put towards other things when there is only 1 class in society.