I'm curious to this because I always see posts on the internet saying that native Americans had their land stolen, that white people are the "real illegal immigrants" and so on. What did the European colonists do differently to make them say this? Isn't what they did the same actions as people like Napoleon, Genghis Khan, or Alexander the Great; just taking land as your own because you have the strength to do so?
Did the Native Americans really have their land "stolen"?
Yes.
Although it is very hard to generalize about a universal Native American experience as it encompasses two continents and multiple native groups, the depopulation and disintegration of Native American polities was an unprecedented action in global history. As /u/400-Rabbits notes in their comment the absolute decline and extinction of Native groups broke with larger historical patterns of warfare. /u/uncovered-history also observes in their comment that:
The warfare against Native Americans was brutal and continuously required that the United States break countless treaties with them, and as a result, many died. This type of systematic warfare is not something we saw in Europe when enemies were fighting each other in war. It wasn't just about conquering and subjugating, but rather it was about decimating an enemy and not allowing their culture and people to survive.
So on macro-level, the depopulation of two whole continents of their inhabitants is quite remarkable.
This segues into what makes this conquest so different than other conquests. Well, take the Napoleon example. Napoleon was a successful general to be sure, but he did not displace and destroy the populations he conquered. If I were a peasant in the Po Valley in northern Italy, I would have to pay more taxes and possibly be conscripted to fight in one of Napoleon's wars after the French conquest. But this hypothetical Italian peasant would not be forcibly relocated to his "natural" homeland in Croatia or Albania. Most other famed historical conquerors may have taken land from other polities, but they did not aim to destroy the population of the lands they conquered. This is not to say that no atrocities occurred in this process of conquest, sacking of cities and enslavement of conquered peoples did occur. And there are debates as to whether or not some wars of the ancient world were genocidal in nature, as you can see in the back and forth in this thread and there were ethnic cleansings like Spain's expulsion of the Moriscos. But the type of wholesale elimination of a people root and branch tended to be outliers in the history of conquests.
Trying to say that might makes right and there was nothing different about the conquest and settlement of the Americas after 1492 is a very lazy and often a disingenuous approach to history. The conquest(s) did depart from prior historical examples in very significant ways.