Correction of your post: The United Church of Christ is the church that took over the building that housed the Pilgrims' first church in Plymouth. And, by the way, the Pilgrims were not the Puritans. The Puritans came later to Boston. Please get my family straight! None of us have anything to do with the UCC. Do not paint us with that one!
We're mincing words here. They didn't take it over - they owned it. They are the successor entity to the original Plymouth congregation.
the way, the Pilgrims were not the Puritans
Puritan is a fluid term which covered quite a variety of different groups.
A generic Church of Englander would have called both the Plymouth and Boston colonists Puritans.