Unlike the Pilgrims, who came to Massachusetts in 1620, the Puritans believed that the Church of England was a true church, though it was in need of major improvement. ... The first groups came in the Mayflower and were included with the group called Pilgrims. ... What could have been stopped progressed into a community tragedy. ... When the first religious pilgrims came to the new world in 1620, to Plymouth, Massachusetts on the Mayflower, it began a wave of such trips. ...