Theonomy is a term for the belief that the moral law of God is to be applied as a standard of righteousness for governing individuals and society. The term comes from the Greek for "God's law" and is the concept that all of the moral laws (those excluding the non-ceremonial and dietary laws) given to Moses and recorded in the Pentateuch are binding on people of all nations forever. Theonomy posits God's law as the only just standard for regulations in every human institution: family, church, and state.
Theocracy is the term for a nation ruled by God and God's law. Theocracy does not imply rule of the state by the church. The proper term here would be an ecclesiocracy. Although the church and the state are separate spheres of government, both are to be ruled by God's law.
Detractors of theonomy and theocracy like to argue that the civil law and its sanctions were limited to Old Covenant Israel because there was no separation of church and state in Israel's theocracy. Even a casual survey of the law of Moses disproves this conjecture. The Old Covenant commands that "alien and sojourners" in Israel, even those who were uncircumcised heathen, were bound to the civil law (Lev. 24:22).
Yet these foreigners were not required to keep most of the ceremonial aspects of the Mosaic law (Ex. 12:43,44,48; 9:33; Deut. 14:21). Only the circumcised were allowed to participate in the Passover, the old covenant communion meal. The two "marks of the covenant" separated members of the "church" from members of the "state." There was also a separation between the priests of the ceremonial law, the Levites, and the magistrates of the civil law, the elders and judges (Lev. 14:35; 27:11; Deut. 1:16; 16:18; 19:12; 21:2; 25:1).
In the New Covenant, the primary purpose of the church is to minister God's grace in the world. Christ's commission to the church was to preach salvation to the nations (Matt. 28:18-20). The Apostles were given the keys of the kingdom and the sword of the Spirit, the Word of God, in order to carry out the Great Commission. The state is to be a minister of justice (Rom. 13:1-7). It alone is given the sword of power to execute vengeance on those who would violate the law of God as expressed in the laws of the civil sphere. The church is never to control civil government, but may instruct state proceedings with biblical counsel (Deut. 17:8-13). The church is also expected to train godly men for civil leadership.
The problem, of course, with the colonial Massachusetts "theocracy" was that it was not a true theocracy with separation of powers, but an ecclesiocracy. Cotton Mather wrote: "Yet, after all...in this world a Church-State was impossible, whereinto there enters nothing which defiles."
On the other hand, it was this experiment with self-government which finally led to the emancipation of the colonies from the tyranny of the British crown in later years. In all fairness to the Massachusetts Puritans, we must...