It is true that the Mayflower Pilgrims were not Puritans, but they were very similar to the Puritans in that both groups were devout Calvinistic Christians. The difference between the Puritans and the Separatist Pilgrims was that the Puritans were content to remain within the State Church of England and try to purify it, while the Separatists decided that they could not remain with the State Church of England so they separated from it.
As to the first Thanksgiving in Plymouth, there are two primary sources from Pilgrims who were actually there, Edward Winslow writing in “Mourt’s Relation” and William Bradford writing in “Of Plymouth Plantation, each of which can easily be accessed on line.
https://faculty.gordon.edu/hu/bi/ted hllderbrandt/ nereligioushistory/brad
There is also a passage in “Of Plymouth Plantation” under the year 1623 which describes the setting apart “A solemn day of humiliation. to seek ye Lord by humble & fervente prayer, in their great distrese. And he was pleased to give them a gracious & speedy answer, both to their owne, & the Indeans admiration, that lived amongst them.” [sic] Afterwards, “the Lord sent them shuch seasonable showers, with enterchange of faire warme weather, as, though his blessing, caused a fruitful & liberall harvest, to their no small comforet and rejoycing. For which mercie (in time conveniente) they also sett aparte a day of thanksgiveing.” [sic]
So, as for the first Thanksgiving according to “Mourt’s Relation,” there was a harvest celebration and a recognition of the goodness of God for it. In the section from “Plymouth Plantation,” recorded under the year 1623, there was a solemn day of humiliation, to seek the Lord by humble and fervent prayer, followed by an acknowledgment of God’s gracious and speedy answer and subsequently the setting apart of a day of Thanksgiving to God for His mercy and blessing. It is actually pretty close to what I was taught in elementary school 60 years ago.