Williams did not differ with them on any point of theology. They shared the same faith, all worshiping the God of Calvin, seeing God in every facet of life and seeing man’s purpose as advancing the kingdom of God. But the colony’s leaders, both lay and clergy, firmly believed that the state must prevent error in religion. They believed that the success of the Massachusetts plantation depended upon it.
Williams believed that preventing error in religion was impossible, for it required people to interpret God’s law, and people would inevitably err. He therefore concluded that government must remove itself from anything that touched upon human beings’ relationship with God. A society built on the principles Massachusetts espoused would lead at best to hypocrisy, because forced worship, he wrote, “stincks in God’s nostrils.” At worst, such a society would lead to a foul corruption—not of the state, which was already corrupt, but of the church.
The philosophy Williams developed to deal with the struggle came to be called "the separation of church and state." And although the concept is a part of what the United States is about, people have argued over what it really means ever since. Smithsonian has an extensive article on Roger Williams and his ideas. Link