Yes, but these powers are accessible to everyone, depending on their class and magical gear
'Class' = package of superpowers (i.e., powers that are not accessible to 'normal people' at all); 'magical gear' = devices / gadgets / thingies that grant or enhance mundane abilities and/or superpowers. Many 'supers' happen to have been normal humans anyway, if not for very similar 'boosts', as it so happens. fwiw.
, so despite the trappings, they're still humans harnessing the natural forces that exist within that world. OK, so you can throw fireballs. It's magic that allows you to do that. It's also magic that can protect you from them. It's also magic that allows you to travel the planes. Sure, you can play a sorcerer, where magic is something you're born with, but that gives you no advantage over the guy who was born a normal human and studied magic until he became good at it.
So, in other words, just as is the case with superpowers, those can come from birth onwards, or from another source, with specialised - and very much
out of the ordinary - training being just one of these. Replace the word 'magic' with 'superpowers' (in fact, they're exactly the same thing anyway) and it's all clear as can be.
Superheroes assumes a mundane world that exists alongside the heroic world where the only way to have powers is to be born to them (or get bit by a special radioactive gecko, or get accidentally bombarded by Doofus rays, or what have you).
That depends entirely on ruleset, campaign style, comic [or comic-like] influences (if any), setting, characters made, etc.
In other words, a normal person generally won't stand a chance of becoming one unless the GM is engaging in some necessary deux ex machina, or stand a chance against them. To me, this demeans the relevancy of ordinary humans. In D&D the assumption might be that PCs are a cut above the average person, but that usually means that they're in the top percentages of strength, Dexterity, Intelligence, etc. but it does not mean that they have something that is clearly far and away superior to any other person.
Um, except that they do. How many D&D settings are truly chock full of Wizards, Clerics, Druids, etc. -
as the norm, I mean. . .? What's up with how that conflicts with nearly every single D&D (or related) setting I've come across, and even rulesets themselves (e.g., minions, Action Points, Conviction, normal humans / normal men, NPC classes or roles, totally unstatted 'normal' NPCs all over the place, descriptions of typical demographics. . .?
For instance, in 3e-based settings, every single NPC with average stats
could be a Sorcerer, let's say. And every second one could fling Magic Missiles around (f'rex). How would it be if (for example) every second human in a given setting did just that (i.e., lobbed three Magic Missiles a day around). . .?
D&D characters are, regardless of edition, *extremely* different from normal folk. The books themselves, even without setting material brought in, make this abundantly clear, over and over. Edition after edition.