What does it mean to have super powers? Characters who qualify as "super" often have many or all of the so-called "flying brick" qualities, like flight, invulnerability, energy beams, super speed, heightened senses, super breath, etc. Super powers always have a plausible explanation as well: Gamma radiation, radioactive spider bite, an "accident"-based origin, mutation, aliens, magic weapons, and so forth.
But super powers are just explanations for why some characters in fiction have permission to break the laws of believability. Normal people can't change into giant, green rage-monsters or melt steel just by staring at it, but we love stories about people who can.
However, we also love stories about ordinary people who can do extraordinary things. Characters like Batman, Iron Man, Lex Luthor, Hawkeye, and Conan – hell, even Rambo, regularly break the laws of believability and get away with it, even though they haven't been given the "super powers" pass. Except they have been given permission; they just have different explanations for what they can do. Any character capable of extraordinary feats has super powers, regardless of whether or not those abilities are defined as super powers within their respective universes. Peak physical conditioning, special combat training, genius intellect, and technology are all just different kinds of super powers.
Batman is a great example. Fans love to point out that Batman is just a "normal" man who can die from anything that could kill you or me. The thing about Batman is that his vulnerabilities are the only thing the reader has in common with him. Everything else he does is super human.
"But," you may argue, "Batman's abilities are all within the boundaries of what humans can do." In other words, he can't juggle dump trucks or race a spotlight to its target. True, but just because his abilities are not exaggerated in that way doesn't mean he's not super human. Usain Bolt is pretty fast, but I doubt he can dodge point-blank gunfire like Batman. The Flash can dodge bullets because his super power explains why he is allowed to do that. No problem. Batman can also dodge bullets, except his explanation is "peak physical conditioning", and it ultimately provides the same permission (dodging bullets) that super speed provides. Granted, Batman can't tap into the speed force or travel through time on a treadmill, but his character doesn't need to do things like that, so he has powers that operate within the bounds of what his writers need him to be able to do. There are other heroes who can fit under this Batman archetype, such as Hawkeye and Black Widow, who derive their powers from conditioning, combat training, and special weapons.
We've become quite comfortable with "special forces training" as an explanation for super human abilities. In action movies, every hero who has "former SEAL" in his resumé can blow up any building, shoot down armies, pilot any vehicle, beat the crap out of mooks with peerless Kung Fu, and bang hot girls with impunity. When I was a kid, my dad used to let me watch all those macho action flicks from the '80s, and he taught me to laugh at how ridiculous they were. There's a scene in "Commando" in which Ahnold bucks about 12 security guards off of him in Incredible-Hulk-fashion, rips a phone booth out of the wall (with someone in it), and then swings across a crowded mall like Tarzan. How is that not super human? And the explanation is "special forces training." My dad used to say, "You know why Arnold can shoot them but they can't shoot him? Because only Arnold gets real bullets. The rest of'em shoot blanks."
Conan the Barbarian is a super human on several levels. He's a master warrior and thief. He can track deer through fallen autumn leaves without making noise. He can sleep naked in the snow and find no discomfort. He is also able to sleep so lightly that he pretty much remains conscious and aware of his surroundings even while asleep. In fact, his barbarian instincts serve as a kind of early warning system, not unlike spider-sense. Conan bragged that he once broke the neck of a Cimmerian bull with his bare hands – and he did it when he was 15. I once found a message board where fans were trying to explain to a doubter how Conan actually did this, and none of them had a good answer. The best answer is that Conan has super strength; it just isn't as exaggerated as Superman's.
Not all non-superpowered super heroes rely on training and physical conditioning. Iron Man and Lex Luthor come to mind. They each have one super ability (two if we count bottomless financial resources as a super power). They're both super geniuses. Yes, I know Luthor is primarily a villain, but anyone who can claim the title of "Superman's arch nemesis" deserves to be part of this discussion. Tony Stark doesn't have any "natural" super powers, so he builds his own. Using his technology as an explanation, he has super strength, flight, invulnerability, energy beams – basically he's a flying brick. Lex Luthor has done the same thing. Through his intellect and money, he's built the technological means to duel Superman, and that's no mean feat. There are real super geniuses in the world, but none of them have developed weapons like Stark or Luthor. Technology equals super powers.
The "normal" super heroes mingle with the big shots all the time, and we tend to give those characters an extra notch of respect because they've mastered themselves so well that they can run with the big boys. But really, Hawkeye and Black Widow are as super as Thor and Hulk, they just have different abilities. Nobody makes it onto a super team without being super.
I think Batman is the best example of these kinds of "non-super" super powers. In addition to peak physical conditioning and training, he also has the super genius thing AND he has limitless financial resources. In the upcoming Batman vs Superman film, I feel like Superman is really the underdog in this fight because he doesn't have the resources, the technology, or the training that Batman has. If he somehow defeats Batman through sheer heart and determination, I'll be surprised, but I don't think Snyder would risk the ire of so many fanboys by giving us an outcome like that because if Superman beats Batman, it just won't seem believable.