The differenetiation has already been laid out.
The Avengers are accepted to the degree that they are because they're a well known, mainstream outfit who are mostly humans who have been enhanced by science or tech. The main ones were public figures and even registered government operatives, with Peter ironnically being the only one with a secret identity. The ones who are less (or more) than human have to be reigned in (Hulk, Wanda) and assimilated into the group lest they be outcasted and hunted down.
While some mutants can blend in with the rest of humanity, a lot of them cannot. It's either apperance or they have abilities that can't be explained away with science or tech. The minute the world finds out that there are people out there who are BORN with abilities, as in
a whole different race/species of "living weapons of mass destruction" the fear mongering by agencies like the DDOC and A.I.M. will ramp up as will the xenophobia.
The MCU does not stick strictly to the source material, for good reason in some cases, as seen in the show this thread is about. And according to the source material, the celestials are at the root of all the potential for mutation in the human genome. Why we need to piece out that Inhumans, another race of genetically engineered super people are somehow their own thing is reduntant, in the comics let alone on screen.
I addressed all this above and agree with you, I just don't deem it nessecary to try and explain to the casual audience the nuances of mutation. Even in Ms. Marvel the show you have clandestines/jinn, the x-men music..does the DDOC know or care about Kamala's DNA? How much time should be spent on wether she's a genie, a mutant, mutate or an inhuman...these are just labels that deliniate the genetic potentials.
Using the Avengers game for example, the people who got exposed to the mist started manifesting powers and abnormalities and began getting rounded up, what's really gonna seperate them from mutants on screen? They gonna put them in two different camps?
You don't have to slice and dice the terminology depict the public freak out that's going to happen when there's an acceleration of mutation, wether it be through birth or other catalysts, the public is going to freak the fukk out and start rounding these people up.
If something like that happens at an elemenatry school, Civil War 2 will be about 'mutant' registration and concentration camps instead of reigning in super soldiers and science experiments.