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Quakers and Puritans had very little in common in their beliefs. True both left England for religious freedoms. But aside from this, Quakers and Puritans had little in common. Puritans condemned Quakers in fact, persecuting them just as much as one of their "witches." Even though both are Protestant groups, one could say that the Puritans had more in common with radical Catholics than with other Protestants. Below is link to a chart of the two groups and the beliefs back to back. Hope it helps.
they were both here in America for religious reasons and rights
No, but they are historically related. Puritans preceded Quakers in the religious ferment of Britain's 17th century. Both groups rejected state-church enmeshment and episcopal governance; 17th-century Quakers went on to reject prayerbooks, outward ceremonies of all kinds, military service, and a paid priesthood. Nevertheless, both groups agreed on the central role of the Bible and on the importance of a disciplined life. Quakers: Religious Society of Friends: a Christian sect founded by George Fox about 1652; commonly called Quakers. Puritans: A dissenting movement within British Protestantism that developed in the late 1500s. Puritans settled in the New England area in the early 1600s. Characterized by strict focus on the Bible and the authority of God, both personally and socially, severe restraint in behavior, and hard work. Early American Puritans saw nature as "a hideous and desolate wilderness" to be walled off or controlled and tamed. Later Puritans, such as Jonathan Edwards, began to see beauty in nature as a manifestation of God. Definitions quoted from Related Links.
both faced religious prossecution from the church of England and they went to North America to escape the beliefs of the church of England.
The religious group was called puritan because they were supposed to be "pure." They had very strict rules about religion and did not let their people change religions. In a way, they were somewhat the exact opposite of Quakers. Puritans were sometimes flogged if they did something wrong.
Roundheads
John Winthrop lead a large migration of Puritans. This started in England and the beliefs were strict.
The document was the Mayflower Compact. This was created to insure that the Pilgrims all agreed to follow a common set of rules.
They were professional artisans
Mostly Catholics and Quakers
The Puritans were more common in the North Colonies, I believe.
They were both evangelists and explorers