There are certain genres where you could develop powers. Wuxia for instance. But if there were a single method, you don't end up with the happy muddle that constitutes superheroes. Martial arts would lead to wuxia or something like it; some kind of magic study to fantasy; gadgets to science fiction, even if it's the Earth-bound equivalent of planetary romance or space opera.
But if you had half a hundred difference ways, where hard work and study (with talent providing some help) anyone could develop superpowers, from a ninja who can teleport to a paladin who can dispel evil to an alchemist who can turn lead into gold, it would come across as superheroes. Although a very odd one. Anyone could be a super, and not in the sense that some works have, where anyone has the potential if it's properly triggered. (And probably the muggles would be just as envious as they would be for dumb luck. Knowing they could do the same leads to resentment of those who showed them up.)
How hard it takes, how reliable the time frame is, whether the paths are miscible at all, whether you can ever switch from one to another -- there could be a lot of possibilities just varying the setting.