How does Chief Seattle’s view of the relationship of humans to the natural environment differ from that of the European settlers?

The answer to this question can be found in the famous speech that Chief Seattle (Si'ahl), a Suquamish chief in the northwestern United States, supposedly gave in response to offers by the federal government to purchase lands belonging to his people. While the speech is probably apocryphal, it does outline several typical differences between Native and white conceptions of the land and the environment. First, Si'ahl says that his people have an organic connection to their lands that whites do not:

To us the ashes of our ancestors are sacred and their resting place is hallowed ground. You wander far from the graves of your ancestors and seemingly without regret.

Because the lands hold the bodies of their ancestors, to abandon them would be a spiritual catastrophe, one which would violate a sacred trust between the living and the dead. Whites, as Si'ahl makes clear, felt no such connection. They could move from place to place, turning their backs on their past. He makes it clear that every aspect of the environment has spiritual meaning to the Suquamish people. "Every hillside, every valley, every plain and grove," he says, "has been hallowed by some happy or sad event in days long vanished." Whites, viewing land and their environment as a commodity to be exploited, had no such connection to the land. In another communication, this time a (similarly dubious) letter to President Franklin Pierce, Si'ahl allegedly expanded on this theme:

How can you buy or sell the sky—the warmth of the land? The idea is strange to us. Yet we do not own the freshness of the air or the sparkle of the water...

While the authorship is highly debatable, Si'ahl's view of the natural world is fairly consistent with what many Native leaders tried to explain to whites who demanded that their lands be ceded or sold. Native peoples could not view land as simply real estate to be bought and held in perpetuity or until sale. It is not exactly true to say that Si'ahl lacks an understanding of private ownership of land—he seems, in these passages, to have a highly sophisticated grasp of this concept. But it is one, he says, that as a Native person, he cannot share.
http://www.halcyon.com/arborhts/chiefsea.html

https://www.archives.gov/publications/prologue/1985/spring/chief-seattle.html