By both. The first Indians Europeans in North America encountered were the Aztecs, Toltecs, etc [with a governmental form not totally alien to the Europeans], the Powhattan Confederation, the [later named] Wampanoag Confederation, and the Iroquois Confederation [who are now claiming they gave Franklin and the boys the idea for our governmental form.
European settlers wound up fighting the Powhattans [Opechancanough’s Wars], the Wampanoags [King Philip’s War], the Pontiac Confederacy, and at least four of the Six Nations of the Iroquois. From the beginning, Americans treated with Indians as separate nations, which the Indians seemed to prefer [logical in a society based on communal use of resources].
The mistake the U.S made came under Grant, when the cultural separatists won out over the assimilationists, and the old system continued. Indians should have been integrated into the society as individuals, given citizenship, land allotments under the Homestead Act, and temporay support and assistance in transitioning from hunter-gathering to agriculture [or in the case of the Cheyenne, Pawnee and other tribes, transitioning back to agriculture].
No, Grant's Peace Policy was completely oriented toward assimilation. At the end of the Civil War the west was on fire. During the war troops had been withdrawn east to fight the South. The Indians took the opportunity to attack Whites. This led to retaliation by Whites which led to retaliation by Indians. Chivington's attack at Sand Creek ignited a two year rampage of murder and rape and theft that engulfed the Great Plains and the mountain west.
The country was tired of war, short of money and short of troops. Reconstruction and occupation of the South was the primary focus. Instead of trying to militarily defeat the Indians, Grant sent his "peace commanders" west and focused on a process of assimilation.
To do this he first had to stop the depredations. It was determined to assemble the tribes on areas exclusively reserved for them, temporarily support them and teach them agriculture and trade. Against howls of protest he took authority away from the military and gave it to religious organizations. This was the impetuous for the Medicine Lodge Treaty et.al.
The Peace Policy was contentious from the beginning. Settlers continued to suffer raids and demanded military intervention. The Indians splintered, some honoring the treaties, some openly violating them and some taking advantage of the sanctuaries they offered to raid, rape and murder and then retreat into peaceful populations. The reservations were often underfunded and much of what was available was stolen by the agents.
Several attempts were made to break the power of the tribes by treating Indians as individuals and these generally ended in disaster. Individual allotments were made of farm sized plots. Lack of promised farm impliments and support doomed most. Others were sold at rock bottom prices to fuel drunken sprees. There were few successes to point to.
The Peace Policy finally collapsed into open warfare. Most were already on reservations but those who were not were forced there by brute military power. With this change in emphasis from domestication to subjugation the attempts at assimilation seemed to lose direction and purpose. They fell into a long period of hopeless fatalism.