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Please correct me if I have misconceptions, I have mostly only seen the movies (I've read a few comics, mostly of the superhero side. Would like to get more into that.).
The marvel universe is home to both mutants from X-men, as well as various superheros like the Fantastic 4 and the Avengers. Some people are both (Though for licensing reasons it may be along time before it is said in those words in a movie).
It seems like the difference between a Mutant and a Superhero (/Super-villain) is almost entirely arbitrary (with some exceptions for equiptment base heroes (eg iron man) and aliens (eg Thor), etc). It seems like just looking at most Supers/Mutants it would be hard to tell one from the other. It being largely a matter of origin story.
However Mutants seem to be immediately assumed to be problematic/bad by the general populous (or at least a large amount of it), Where as superhero/villains are judged on their actions. (and indeed often get away with a huge amount of collateral damage.)
Is it just that the different franchise focus on different aspects of the story, but without that focus they are in fact treated the same? Ie Supers are actually just as contentious as mutants, but the contention is not part of the main story, where as X-men has strong themes of acceptance.