Puritans in America and Cromwell

by FlipsManyPens

I have been listening to Food: A Cultural Culinary History (https://www.audible.com/pd/History/Food-A-Cultural-Culinary-History-Audiobook/B00D8EMBVQ) and he mentions that the Puritans which came to America were basically the same ones which took over England after the civil war. Did any American puritans return to England once the threat of persecution was presumably gone? What did the two groups think of each other?

TRB1783

It looks like /u/Oldworldglory has compiled a few answers about this here. See if those help, and feel free to respond here if you have any further questions.