I think the Pilgrims were Congregationalist.
The Puritans who settled in Boston about l0 years after the Pilgrims landed in Plymouth had a different view of organized religion, and I believe they brought with them the Presbyterian Church.
Correct me if I’m wrong.
I thought that prior to the English civil war Presbyterianism was pretty much a Scottish denomination. Both the Pilgrims and the Puritans came mostly from East Anglia.
The Puritan movement of course included Presbyterians, as well as Congregationalists, and, even Particular Baptists. One cannot pigeon hole the movement as being only Congregationalists... more like, the most serious and radical of Protestant British and European colonists at the time were Calvinistical, and therefore interested in purifying a corrupt Church. And even Anglicans at the time, were very influenced by Calvinism (Anglican Christianity being originally described as the middle ground between Calvinism and Lutheranism (no, not Roman Catholicism).
Officially, the Puritan party originally wanted to stay Anglican, and purify the English Church, but, little by little, serious Calvinists found it impossible to stay...and broke away (even if by just going to America). Presbyterianism after all only refers to the practice of governance by Elders (a concept originally developed by Calvin)...(not fully democratic like Congregationalism, nor hierarchical like Anglicanism or Rome...) which is, after all, a foretaste of Representative Democracy....
Calvinists is a term broader than just English Puritans, as it consists of far more than Englishmen, but, the “Puritan movement” was fully fledged Calvinist...and the most influential movement across denominational lines in pre-revolutionary America.
So close were the Puritan Congregationalists to the theology of Presbyerians, that Congregationalist and Presbyterian pastors would trade off preaching at each other’s churches, or even be hired by one or the other...there really wasn’t all that huge of a gap, in America at least.
Rule of law...(originally thinking of God’s moral laws) applying equally to king or commoner is one of the main subversive elements of Calvinism to monarchy.
Interestingly, I’ve read that in China today, Presbyterianism is a favorite form in highly educated house churches...of course due to many Presbyterian missionaries there (like Eric Liddel) before Mao, but also due to the fact that Calvinist theology gives the most logical base for democratic ideas...