Puritanism was increased tremendously in England during the later years of James I. Puritan and Pilgrim was not synonymous terms. The Puritans were those who sought to purify the English church and to modify forms, while remaining with in it. The word "pilgrim" has required a religious meaning. It was applied only to the Separatists or Independents who settled at Plymouth because of their migration. But eventually the Puritans became independents, not only in America, but in England as well.
There were many companies entering New England, but the Puritans mass departure was yet to begin, as a large number of them were now ready to join the colony, to them it was deemed far more satisfactory to have a royal charter than a plain land grant. A charter was therefore secured from Charles I in March 1629. This new company was styled the Governor and Company of Massachusetts Bay in New England. The government was to be placed in the hands of a governor, representative governor, and eighteen assistants, to be elected annually by the company.
Accordingly, a small party of leading Puritans met at Cambridge in august 1612 adopted the "Cambridge Agree
remaining within the colony. The marks of a Christian were judged by their outward
Underwood, Devon Women’s Roles in the American Colonial Period http://info-center.ccit.arizona.edu/~ws/ws200/fall97/grp11/part1.htm