This article has a nice synopsis. It is from a Catholic point of view, but the intro, which builds off of the entry in the Encyclopedia Britannica, is general:  The American form: “as implied in the Constitution of the United States, was supported by a tendency to leave to the church, set free from state supervision, a maximum freedom in the realization of its spiritual, moral, and educational tasks.” This puts emphasis on freedom of religion, allowing the Church to operate free of State control or interference. The restriction is put entirely on government, with no restrictions on religion at all. Government is prohibited from interfering in the internal affairs of religion, but religion is free (through democratic and parliamentary processes) to interfere with the internal affairs of government.  What is contested in this essay, however, is the French form