The Pilgrims ( called Brownists, after their much-jailed founder Robert Brown) can be lumped into the Congregationalist end of the Reform movement: they allowed a great deal of freedom to individual congregations to decide on liturgy, etc. The Puritans wanted to reform the Church of England, make it conform to Calvinist theology. The Brownists didn't believe they had to reform the Church, that it was OK to have separate , independent congregations.

The basic point is what we would call tolerance, and what then would be called liberty of conscience. In the 17th c., differences in belief would be very troubling for most people: heresy was something that could condemn not only the heretic to everlasting torment in hell, but could endanger the chance of an afterlife of anyone who listened. The Puritans in this were like most people: for them, there was one true church to which everyone had to belong. This is why the small congregations of Brownists in England, staying away from the Anglican church and meeting in secret, were regarded almost like criminal gangs, were hunted down, the members beaten and jailed. In the Puritan Boston Bay colony of the 17th c. it was hard to maintain this level of intolerance. There was no Church of England governance present. Schisms happened constantly, as once people landed on the Massachusetts shore they often had many bright theological ideas ( as witness Anne Bradstreet and Roger Williams). In the New World there was little difference between a Calvinist congregation that wanted to reform a church that wasn't present and one that wanted to be separate from a church that wasn't present . And so eventually Plimoth was absorbed into Boston Bay.