When the Indians fought another tribe, they killed as many as they could for as long as they could.
That is almost completely wrong. In fact, many tribes practiced almost bloodless ceremonial battles where nobody was expected to die on either side. Unlike in Eurasia, the population densities of most tribes simply did not allow for that kind of warfare. Even the ones recognized as the most bloodthirsty like the Aztecs did not fight that way.
In general, if it was a battle and not just a skirmish by randomly meeting groups it was mostly just a show of force by each side. Not unlike a European battle where they would taunt each other before forming their lines and charging. And after enough were wounded or killed, one side would retreat and the battle ended.
But the almost bloodless combat was actually largely done by the Plains tribes. The Blackfoot were particularly known for this kind of warfare, as were the Crow, Kiowa, Cheyenne, Comanche, and even some tribes of the Apache and Lakota. After all, that is where the very terms such as "Counting Coup" and "Coup Stick" came from.
Not unlike a modern military training exercise with MILES gear. Both sides line up, but instead of armed with spears, bows and war axes they held "coup sticks". And the idea was to defeat the enemy by striking them with the stick then withdrawing. Those who were struck were also by tradition to withdraw, and the bloodless battle would continue until only one tribe had warriors left. That side was the winner, and then dictates the terms (normally related to land and who could settle where).
In fact, the last Crow War Chief only died in 2016. That was a particular honor, only awarded to Crow Warriors who accomplished four tasks. First, to count coup against an enemy and allow him to live. Second, to take an enemies weapons. Third, to lead a successful war party against an enemy. And forth, to steal the enemies horses.
Joe Medicine Crow is more than a bit of a legend, accomplishing all of those actions against the Germans in WWII. And even more interesting, his nephew Carson Walks Over Ice accomplished almost the same thing in Vietnam. And while he thought he had accomplished all four feats, his stealing two elephants from the Vietcong was dismissed, as quite obviously elephants are not horses.