This.I'm not really sure I agree with the distinction anyway - I'd consider Batman a superhero.
And this.Non powered heroes are still superheroes. Batman, Green Arrow, Hawkeye, etc are usually out there not just fighting muggers but a bunch of supervillains, the same as the heroes with powers. I really don't think you can put them in a separate category just because they lack powers. Trying to separate characters into "superhero" and "costumed hero" categories is kind of pointless.
Trying to draw a distinction with the non-powered/street-level superheroes reminds me of when a friend of mine insisted that Batman wasn't a superhero, he was a detective who happened to wear a costume.
Superheroes are a genre of larger-than-life characters who do extraordinary things for the greater good, usually with costumes and often with secret identities. Anyone who thinks that a character like Batman is an an "ordinary person" needs a reality check.
Of course I realize that Batman is not a realistic depiction of a detective or anything like that. No Human could actually do the stuff he's shown to do, and live the kind of life he does without getting killed, especially since he doesn't use guns and avoids killing or permanent injury to others when he fights. Punisher is actually a more realistic version of how a vigilante fighting serious crime with no powers would have to operate.
That said, a distinction is still usually drawn between costumed heroes with no superpowers and other comic book characters. James Bond is larger than life and not realistic but he's not super-powered.