If you ever wondered, "whatever happened to the Puritans in America?", so did I.
The term "Puritan" was never really used much, either by the Puritans themselves, or by the people who disliked Puritans. When the description was new, the fact that it is based on the word "pure" seemed to imply that other believers, well, weren't so pure. And the Puritans themselves just thought of themselves as "the congregation", which is what Puritans became, Congregationalists.
In the 19th century, the word "Puritan" evolved into "Puritanical", which means an overly stern morality, what came to be known as "Victorian". A very straight-laced, "casting sinners out into the snow" attitude. In fact, if you ever read "The Scarlet Letter", it was supposedly set in Colonial America, but it was actually a 19th Century criticism of "Victorianism", which was fictionalized as "Puritanism". People back then knew that, but since then we seem to have lost track.
So, Puritans were neither Pilgrims nor Victorians.