@contrex,
Not all historians agree that the separatists can reasonably be distinguished from the low church Puritans. The question is interesting for another reason, though, as it emphasizes the "New England-centric" view of American history. Jamestown was settled in 1607, more than a dozen years before Plymouth, Massachusetts. In the United States, the independent or separatist Puritans became the Congregationalists, and most of the descendants of the Puritans of Massachusetts Bay became congregationalists, along with their separatist brethren, as well as the independent congregationalist dissenters--those who were not necessarily Puritans, but who were the backbone of the Eastern Association in the civil wars, and the principle source of Cromwell's troopers.
In addition to the Jamestown settlement, there were small settlements of fishermen on the Massachusetts bay, and along the coast to the north. Those fishermen were English, Basque, Portuguese and French. They are totally ignored by New England historians, as they were ignored by their Puritan neighbors in the 1630s. They were a "necessary evil" for John Winthrop (the so-called Pilgrims had just ignored them entirely), as they were the only source of foreign exchange and specie to circulate in the colony. That became even more important after 1640 when they were cut off (commercially) from England, and needed to trade for the specie to by arms, powder and shot to fight the indigenous population. In Virginia, the settlers were attacked by the aboriginals. In 1619, the Virginia Company of London, before it went bankrupt, sent out settlers to what became known as the Martin's Hundred Plantation (that's a year before the holy rollers showed up in Massachusetts Bay). They were attacked and nearly wiped out aboriginals in 1622.
In Massachusetts, the Puritans decided, conveniently, that the aboriginals were in league with Satan, and so justified attacking them to get good land for pasturage and crops. In 1637 and -38, they went to war with the Pequot (or Pequod) tribe, and the Narragansett tribe, who had originally threatened the English settlers, allied themselves to Winthrop's colonists. There was a terrible slaughter of Pequot on the Mystick River, and horrified, the Narragansett withdrew from the alliance. That was a good excuse to declare them to also be in league with Satan, and to attack them. The Narragansett were the larges Algonquian-speaking tribe in New England, and the extermination of some, and the driving off of the rest gave the Puritans the "hammer hand" in dealing with aboriginal tribes after that.
To pay for their wars, the Puritans relied on the foreign exchange from the despised fishermen who were already established on the Massachusetts bay, or who arrived after 1620. In Virginia, they relied on tobacco, which John Rolfe had introduced as a cash crop in 1611, nearly a decade before the holy rollers showed up in Massachusetts. In both cases, it was expedient to sail to the Dutch or French settlements in the West Indies, where arms, powder and shot could be obtained. Even though the price was high, it was basically smuggling by everyone's definition, so there were no import duties, and the Virginia tobacco proved to be particularly locrative. The good Christians of Massachusetts soon learned the wisdom of distilling demon rum from the un-dutied sugar they bought from the French and the Dutch. They were still doing that almost 150 years later when the Sugar Act of the 1760s became a major grievance for the Americans in the years leading up to the revolution.
Basically, though, that test peddles the Protestant, English point of view of New England, and fails to take notice of anyone or anywhere else.