In what ways did the early Euro-American colonists employ a land tenure system that was similar to the Native American land tenure system?

First, we should say that the range of experiences in the colonies was so broad that it is hard to generalize about either Native systems of land tenure or those of Europeans. Overall, Natives lacked the concept of individual land ownership in perpetuity that existed under European legal traditions. Lands were "owned" by Native villages, and, as in Europe, they were fiercely fought over, but they were generally held in common. Europeans had an older concept like that (it was actually comparable to the land-tenure traditions that characterized manorial relationships), but by the time Europeans came to the Americas, these traditional concepts had given way to modern understandings of land ownership. Even ordinary people who settled on backcountry lands nominally controlled by large land speculators believed that their "improvement" of the land (by establishing farms there) gave them permanent title to it. This was a concept that simply didn't exist among Native peoples, and it became the source of tensions in the early seventeenth century, when land treaties between Natives and colonial authorities were mutually misunderstood.
https://www.history.com/topics/colonial-america/thirteen-colonies