Were the Pilgrims really in New England, or in New Netherland?

The Pilgrims landed in New England. The Dutch established New Netherland in 1609 in and around the Hudson River valley. The main city would become New Amsterdam, and it was meant as a trading site. The Dutch were one of the most religiously tolerant people in the Old World, and this practice would continue in the New World, as various groups would settle in New Amsterdam. Even when the area was taken over by the English and renamed New York, the region would still remain culturally diverse.
New England was north of New Amsterdam. The Pilgrims meant to settle around Virginia in 1620 but were blown off course and settled in the Massachusetts Bay area. They claimed the land for England and named it New England. While there may have been conflicting land claims, the area was always firmly under English control. The Pilgrims did not practice religious tolerance and even banished some of their own members who did not practice according to their strict rules.