There's plenty of overlap, but I would think a superhero being a type of costumed crimefighter is more true than the inverse. But perhaps it isn't, a superhero's concern may be more specialized to large-scale crises than actually combating crime.

Either way, superheroes generally operate under specific ethical codes. Their conduct needs to be above board, that they can inspire hope and heroism within the communities they protect. They deserve the love and admiration, because they're a little purer than the rest of us.