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At a very high level economic systems can be classified into 4 groups by two criteria: public or private ownership, and central or decentralized control.
Capitalism as commonly practiced in English-speaking democracies is typically private ownership with decentralized control.
Capitalism as typically practiced in European democracies has private ownership with a significantly greater degree of central control, though still more decentralized than not.
Communism as practiced in the USSR (and its satellites) and China until abut 1990 was strictly public ownership with central control. Since then China has tempered both somewhat, while retaining the broad classification.
Communism as practiced in Tito's Yugoslavia was considerably less centralized than in either the USSR or China.
Fascism as practiced in Germany and Italy from 1920 to 1945 had private ownership with central control.
Of course this classification is the view from 30,000 feet so to speak. Many variations exist between countries, and over time as laws and regulations change. Where and how to draw the distinguishing line for each criteria is more a matter of opinion than not. Any deep analysis requires a detailed examination of the specific legal and regulatory framework, and practice, of a specific jurisdiction over a specific time period.