This collective remembrance is a fallacy. It was the Puritan migration that established this enduring symbol of America that has been reviled and celebrated. A Pilgrim would have shuddered at the thought of being so protrusive. The Pilgrims thought of themselves more as the peculiar, humble children of God rather than Puritan Statesmen or Christian Warriors of the Republic.
Both groups followed the Reformed Doctrine of John Calvin.
Differences begin to appear in their theories of Church Government. The Puritans rose up during the 16th century as the Anglican Church was negotiating the treacherous waters of their separation from the Catholic Church. While many applauded Henry the 8th for his Declaration of Independence from the Pope, many more were insecure about this new system of faith and wanted to preserve as much of the “old faith” as possible. Both Puritans and those who would become Pilgrims wanted to rid the church of tradition, purifying religion by basing belief and practice only on the Bible. Pilgrims began to differentiate themselves when they lost hope that this purification could occur in the Anglican Church. They became convinced that they would have to separate and begin a new pilgramage to build a pure religion.
Practically, the divergence in these two religious philosophies began to appear as the Separatist-Puritans, whom we now call Pilgrims, decided to assemble outside the Anglican Church. This put an unwanted spotlight on their way of life and also brought persecution on them earlier than the Puritans. This was because the Puritans had decided that they could have a more reforming influence by remaining within the Anglican framework. As history has proven, this strategy would be somewhat modified when John Winthrop led his Puritan armada to Massachusetts Bay to become the example “shining on the hill” to the home church.
Another distinction is their attitude toward politics. While neither group shrank from political activity, the Pilgrims were more inclined to have at least a modicum of separation between Church and State. While the Pilgrims believed that secular government should abide by the principles taught in the Bible, they did not believe that the state had the authority to meddle in spiritual matters. This is evidenced in the Mayflower Compact which seemed to show religious tolerance to those passengers who did not share the convictions of the Pilgrims. Conversely, the Puritans felt a great need to work within the political realm as much as the spiritual in order to bring both areas under the control of the guiding principles of the Bible. The religious intolerance of the Puritan political machine was well known for the persecution those who did not agree.
Finally, and most tellingly to the common mind that is not bogged down in religion or politics, the divergence between Pilgrim and Puritan is geographical. The easiest way to tell the difference is to recognize their ultimate destinations on American Soil. The Pilgrims, to whom we generally attribute the First Thanksgiving, were the settlers of the Plymouth Colony, which had its political center in what is now Plymouth, MA and was established in 1620. The Puritans established the Massachusetts Bay Colony a few miles north in Salem and Boston, MA in 1630.
Proclaim Liberty throughout the Land by Edwin S. Gausted, 2003, Oxford University Press