While both are considered Christian religions, The Puritans (a specific group of Protestants) and the Church of England differed on several major theological issues. Members of the Church of England saw the King as the head of the church. This was different from the Catholic religion that saw the Pope as the head of the Church, but the Puritans believed that Christ should be the head of the Church. Puritans didn't want to confess to a priest. They believed that individuals could speak directly to God while the Church of England believed that a intercessor was necessary.
There are other major theological differences, but the most visible differences were probably found in the way services were conducted. The Church of England reads passages from hymns and other materials in Latin. They have ceremonies like candle lighting and confession that don't exist in the Protestant religion of the Puritans. Protestants felt that God should be accessible to all and not just the upper class (Latin was spoken by the upper class but the lower classes were often uneducated).