Theocracy - GOD led. Jn.1:1 In the beginning,.. Immanuel-Christ-Jesus; the LORD, has been involved and overseen, from The Man Adam, down through the Generations. Until 1Sam.8 where the leaders/elders "rejected" the LORD, and requested their "own king, just like the other nations." The LORD made sure that they were aware of this wicked request; and the consequences.
Republic - Made up of Sovereign-States. America for example, was created with 13, individual Colonies that were totally independent: coming together in the case of war. The U.S.C. Tenth Amendment covers the power of the States, and limits the authority of the Federal govt.. The power is vested to the People.
Socialism - Govt. owns or controls via Excessive-taxes, and Regulations. Paying farmers not to plant is about access and control. The People's house[white-house], national-parks, and water-rights all are regulated by the Federal-govt.. A doctrine of Satan and his Kids: to control, or destroy. Controlled by Centralize-govt..
Communism - All property is Publically[govt.] owned: including the People. Work is paid according to the People's abilities and their needs.