I encounter this concept a lot, for example the proverb that states we borrow land from our children rather than inherit it from our ancestors. So why the difference from the Europeans who later colonized the Americas?
Your question reminded me of this old thread:
Not sure if the sources there cover Native concepts of ownership pre-colonization. But it might interest you.
There is a bit of an issue with your question as the Native Americans were not homogenous and had a massive diversity - the tribes along the Atlantic coast such as the Powhatan and the Mohawk had permanent settlements. They understood land ownership much like the Europeans.
Further inland however, more tribes tended to be nomadic, such as the Blackfoot Confederacy. Their perception of land ownership is different. Like most nomadic tribes, they believed in 'temporary ownership' of land.
The American plains were big enough for all of these tribes to wander around without conflict with one another over resources/space. The British desire to constantly push the borders and settle more and more people was completely foreign to these tribes of the plains.
You may also be interested in the problems of comparison: a lot of colonial land-grabs were justified internally (that is, among settlers and between settlers and the European governments) because land ownership had as part of its conception the idea of development. That is, owning land wasn't just having a deed, it was investing time and money into developing the land, putting up fences or planting something and whatnot.
This matters because, fairly or not (depending on the region, the tribal land management systems, so on), the natives didn't "develop" the land to the satisfaction of the Europeans. It's easy to think, "Well of course they just said that to take the land," but really they did have to justify their decisions. Many missionaries at the time actually lobbied for protections for the natives. They were the ones, after all, ministering to the survivors of the fighting.
This principle of developing land is why we still have squatter's rights laws on the books in a lot of states. The squatter often has to prove he or she has "developed" the land in a way the owner hasn't. So if I were to squat on your land and you didn't notice or try to kick me out, and if I then went on to build a fence to keep the neighbor's dogs out, eventually I could be awarded ownership of the land.
One aspect is that ownership was tied more to hunting, fishing, and gathering rights rather than strict occupation. In the Northwest for instance specific fishing areas belonged to individual people or families, and there was a fairly strict economic hierarchy centered around various types of ownership.