What is the difference between Puritans and Pilgrims?

Pilgrim was once (and still is) just a general term for a traveler, with connotations of someone traveling to a holy site or on a holy mission. It is a term that in the US has become ociated with the Puritans who traveled aboard the Mayflower to North America, in order to be to practice their religion (not that they were really all that interested in extending that same freedom to others).