The funny, if sometimes frustrating, thing about how language evolves is that, like water, it tends to take the path of least resistance. Most everyone collectively understand the references being made by these phrases despite them being inaccurate. Thats an indicator that language is evolving, and comic books and anime are coming to be understood as a genre unto themselves in addition to their original definitions as artistic mediums.
And frankly, in the case of anime, this distinction is muddied because the Japanese don't see any distinction between anime and any western animation, and its use in western countries to distinguish is what contributes to it being seen as a genre; likewise with comic books, the "Golden Age" of superhero movies has lead to comic books being mined for adaptation material a lot more than they used to in the past, and as so many of these have turned out to be superheroes or superhero adjacent, that conflates the terms.