The Puritans believed in a strict form of Protestantism called Calvinism. Calvinists believe that God has predestined some people to be saved and others to be damned. They also believe that people cannot earn salvation by doing good works, but only by God's grace.
The Pilgrims were also Protestants, but they were not Calvinists. They believed that all people have the potential to be saved, and that they can earn salvation by following God's commandments.
So, while the Puritans and Pilgrims were both religious groups, they had different beliefs about how to worship God.