Question

What’s the difference between a pilgrim and a Puritan?

Answer 1

While the Pilgrims were Separatists, the Puritans were non-separating Congregationalists -- they believed the Church of England was the one true church and they were loyal to England, but not in the way they worshipped

Answer 2

The Pilgrims were Separatists and the Puritans were non-separating Congregationalist.

Another difference was the time that they came, The Pilgrims came earlier in 1620 while the Puritans came later in 1629-30.  

The Puritans were also mainly upper middle class while the pilgrims were part of the lower class.