What was a key difference between pilgrims and puritans?

Answer 1

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Puritans did not want to separate from the Church of England. They wanted to "purify" it of practices they considered too Catholic.

Pilgrims were also called Separatists. They wanted to break with the Church of England.

Answer 2

June nails it, just wanted to add that the Pilgrims were also called Brownists, after one of their original leaders. Also the Pilgrims settled Plymouth, and the Puritans settled Boston, after they gave up on the idea of purifying the Church of England.