The main difference between the enlightenment ideas and the puritan beliefs is that of how they percieved God.
During the Enlightenment, an emphasis was put on the human reason, skepticism (doubting and examining everything before forming and opinion about it) and primarily science. At the time, people did, in fact, acknowledge the existence of God. However, they believed that God is not in charge of or concerned with their daily lives and does not have a supreme power over people.
On the other hand, Puritans believed that all the people should live according to religion and form their entire lives around the existence of God. As opposed to the people from the Enlightenment era who seem to have merely co-existed with God and acknowledged his presence, the Puritans served God and devoted their entire lives to redeeming for their sins to this, as they believed, supreme being.
