I think in general a "cop" is anyone who enforces the carceral systems of the status quo. Social workers are cops, people who work at homeless shelters can be cops, school teachers are cops. The primary role of superheroes is to "fight crime" and while they do have exploits against foreign terrorists, governments or even extra terrestrial or dimensional threats, that is just like a policeman joining the army in war time. They may be not acting in their role as a cop to fight an external threat but that doesn't change their character as an enforcer of the ruling class.