Ironically, the Pilgrim Separatist and Puritan shared belief in the corruption of the Church of England did not lead to a consensus on the best way to institute reforms.
Convinced that the Church of England retained many of its Roman Catholic elements to its detriment, both groups sought change. The Pilgrim Separatists wanted to either break away completely from the Church of England or to utterly destroy the Church. Puritans wanted to stay within the Church to reform it into an image of New Testament purity; Puritans were not Separatists.
The Pilgrim Separatists originally left the Yorkshire village of Scrooby for Holland in 1608. In 1620, they migrated to Plymouth, Massachusetts and started a colony there. The Puritan Non-Separatists followed the trail to the New World and started a colony themselves at Massachusetts Bay in 1630. At the same time, these Puritans called themselves 'Non-Separating Congregationalists.' They eventually became so many in number that their settlements spread to what is present day Connecticut, New Hampshire, Rhode Island, and Maine.
In 1691, due to practical considerations of survival and viability, the Plymouth colony became incorporated into the Massachusetts Bay Colony. Eventually, dissident groups began to further fragment this temporary 'union.' Out of discord and conflict emerged newly formed groups calling themselves Antinomians, Baptists, Methodists, Quakers, and a whole host of Evangelical Protestant sects well known to present day America.