It's interesting to see how these have changed throughout history: what makes a hero?
Is it your origins? Some stories believe it is something bred in the bones, something inherent to an individual. The very earliest heroes were gods and the children of gods; Hercules, Susano'o, Krishna.
But that's old storytelling. Post-modernism has subverted traditional heroic construction and we no longer favour divine provenance (or, for that matter, prophecy, fate, destiny and other related structures).
Today we see a lot more self-built heroes (especially with the secularisation of literature): characters who have made themselves strong, tough, skilled through their own efforts rather than the blessings of the gods or what-have-you. Contemporary and futuristic heroes are almost all atheists, in practice if not belief. They may have superhuman reflexes and reactions but this is always 'natural' or, at most, created by Man/Technology. These are characters that are The Best Soldiers, The Smartest Hackers, The Most Persistent Cops. They have extraordinary capabilities, but they are at heart "ordinary" people who haven't been chosen or selected by a god or by destiny. Batman, for all his gadgets and intelligence, is an ordinary person. He was never destined or chosen or given a special gift.
People love a rags to riches story. The humble farmer grows up to become a hero but maintains his memory of his peaceful farm or family. We like seeing "heroes" acting like "normal people." That's the rub, isn't it, though? They're not normal people - they're heroes. Heroes are always a little off-kilter, a little out-of-step with the rest of the world. After all, you have to be outside the world to change it - and to challenge others who would change the world for their own ends. Heroes are a kind of autogyro, correcting the equilibrium whenever some mad king or crazed scientist attempts to disrupt it. After all, that's where the word "hero" comes from: to protect or defend.
That's part of why heroes were all divine or otherworldly in origin: not just as an explanation of their power, but also to allow them to reshape the world on their own terms, to fight and defeat enemies in an acceptable manner. When a normal person kills someone, it's murder; when a hero kills someone, it's justice.
So with secularisation has come alternative means of distancing our heroes: traumas (psychological problems), dark secrets, physical alterations (the Cyborg). Again, it serves a dual purpose - justifying our hero's actions while marking him out from the rest of the herd. You can see this in almost any movie and especially in any book or RPG - the protagonist is never quite the same as the others. He's always suffered in some way that makes him separate from the rest of the world.
So extraordinary and ordinary are more then just "is he special." I think it's rooted far more in a different question: "Is he destined?" Is he a self-made hero or did he never have a choice in the first place?