A “scorecard” developed by Mark Noll as set forth in his Books & Culture review of Michael Winship’s Godly Republicanism: Puritans, Pilgrims, and a City on a Hill (Harvard University Press, 2012):
Stuart Anglicans were the monarchs, James I and Charles I, and their bishops who opposed Calvinism, promoted Arminian theology, and moved toward Catholicism in their rituals. To the Puritans they constituted a stupendous barrier to the biblical reforms that the English church so desperately needed.
In Winship’s usage, Puritans were the great promoters of church reform, but who also insisted on maintaining “Christendom,” or the comprehensive church-state unity that had been the European norm for more than a millennium.
Conforming Puritans were willing to live with the Anglican system of bishops if they were free to promote Calvinist theology and biblical preaching.
Presbyterian Puritans wanted to replace the bishops with regional and national synods of godly pastors and lay elders. They expected congregations to aid in selecting pastors, but, once selected, the pastors, acting in presbyteries, were to be the controlling force in promoting godliness. Presbyterian Puritans, closely aligned with Scottish Presbyterians, gained the upper hand in the early years of the English Civil War, during which time they organized the Westminster Assembly that produced the famous Confession and other Presbyterian standards. But these English Presbyterians lost out to the congregational and more radical elements during the ascendancy of Oliver Cromwell.
Congregational Puritans sought churches organized by covenants among members, ministers elected by congregations and responsible strictly to those congregations, and (in New England) church membership on the basis of a testimony of God’s saving grace. The goal was to insulate biblically formed congregations from the corrupting abuses of power.
Determined congregational Puritans dominated New England. Winship says they practiced “separation-without-separating” because they claimed to be only reformers of the national church and because they allowed fellowship with godly Puritans who remained in the parishes of the Church of England.
Militant congregational Puritans were those like in the Salem church who refused to offer the Lord’s Supper or baptism to anyone who maintained fellowship with anyone in the Anglican churches.
Moderate separatists were “separating congregationalists” like the great theologian William Ames and also the settlers at Plymouth. They removed themselves completely from the Church of England but still enjoyed fellowship with the Puritans who shared their general theology, especially with the determined congregational Puritans. For example, the governors of Plymouth (William Bradford) and Massachusetts (John Winthrop) maintained cooperative fellowship with each other in New England’s early days.
Radical separates wanted to break with Anglicanism as completely as possible. The most radical of all was Roger Williams, the sweet-tempered thorn in the side of the Massachusetts establishment. He denounced “Christendom” by name as an anti-biblical system, attacked all ties between church and state, and refused any fellowship (even to pray, even with his wife) with anyone who did not both separate from the Church of England and separate from those who did not completely separate from Anglicanism.