General Discussion

Capitalism, socialism and communism are economic systems defined by ownership of the means of production.

In other words, whoever owns all the businesses in the country defines whether it's a capitalist, socialist or communist country.

In a Capitalist nation, all the businesses are owned by non-government entities, either individual people or some sort of corporation.

In a Socialist nation, all the businesses are owned by The People as a collective whole.

In a Communist nation, all the businesses are owned by the government.

In reality there's no such a thing as a socialist nation. "The People as a collective whole" always means the government, because every communist country refers to its government as The People.

All these other systems like Nazism and Fascism are branches of either Capitalism or Communism.

Strangely enough, the actual National Socialist German Workers' Party, which you know as the Fucking Nazis (FN), was not a socialist party at all. It was a capitalist dictatorship. They used a command economy to direct the resources of the private sector - like having IG Farben produce chemicals needed for the war effort or Krupp make tanks - but the FN didn't own any businesses of their own. It gets better: the Weimar Republic, the first constitutional republic in Germany's history, was economically a communist country. The FN's first act after taking over was to reprivatize everything. China is also a capitalist dictatorship.