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They wanted to change the Anglican Church,while separatists wanted to separate from the Anglican Church
Since most of the Pilgrims actually were Puritans themselves, the answer is yes.
"The Separatists, or Independents, were English Protestants who occupied the extreme wing of Puritanism. The Separatists were severely critical of the Church of England and wanted to either destroy it or separate from it. Their chief complaint was that too many elements of the Roman Catholic Church had been retained, such as the ecclesiastical courts, clerical vestments, altars and the practice of kneeling. The Separatists were also critical of the lax standards of public behavior, citing widespread drunkenness and the failure of many to keep the Sabbath properly. Referring to themselves as the Saints, the Separatists believed that they had been elected by God for salvation (see Calvinism) and feared spiritual contamination if they worshiped with those outside of their congregations, often referred to as the Strangers. In 1608, a community of English separatists decided to escape persecution by moving to Holland, an area long known for its toleration. Dutch society was so welcoming that the Pilgrims, as they had come to be known, eventually feared that they were losing control over their children. In 1620, they set out for a more remote location that would allow them to protect their community. This effort resulted in the founding of Plymouth Colony. Other contemporary religious dissenters, the Puritans, believed that the Church of England was badly in need of reform, but could be salvaged." THIS IS NOT MY WORK
The Puritans did agree with slavery. They saw it as in agreement with the Bible, but slavery in the Massachusetts colonies was regarded as slightly less harsh than the slavery in the southern colonies because the Puritans also believed that it was their responsibility to provide for the slaves' well being, both physically and spiritually.Source: http://www.usconstitution.net/consttop_slav.html
A+ Puritans and Calvinists