One thing that would affect how it would change would be the meta-origin. And if there were more than one source, it would probably affect how the law changed.
Let us suppose that superheroes first arose in the 19th century. Extremely bookish and learned upper-class men revived classical learning including the Greek magical papyri. Just playing them straight would make them wizards a la Dr. Strange, but if they learned how to transform themselves with powers, they could be superheroes. And since they were upper-class and part of high society, it would be natural for them to be treated as part of the government. Perhaps not even licensed -- that would be vulgar. Crimes could be hushed up and would be unlikely to generate legislation. (Especially if they want to keep the lower classes ignorant of the possibility.)
Or suppose the mad scientists made people super-powered for purposes of exhibiting them in a circus. They would have to be more or less willing, because otherwise they would break free. But if they fought crime, they would be irregulars, vigilantes on the street. Police were not exactly respectable in this era, and the ruling classes would be seriously displeased with extremely powerful low-class crime-fighters who picked the crime they fought based on their own interests. Secret identities would be essential, because they would be criminals. Code names might arise from the cheap papers assigning handles to them as to more ordinary criminals. They might, however, have to tolerate them because they were the only ones capable of dealing super-powered criminals.
There would be in-between cases. Suppose up-and-coming scientists were involved in making superheroes. Much less respectable, in the vulgar "stinks" of science, though perhaps they could be co-opted. At least if they were willing to be brought into the ruling class. They would probably be licensed, if they were respectable sorts, if only -- to deal with those of them who go renegade.
Or esoteric cults that gained power and fought against strange beings that threaten the world from etheric realms, and perhaps against their own renegade members. And solemnly warned about getting back into the exoteric powers of the world as a temptation to fall from their high calling and also forming an obstacle to drawing people into the cult. However upper-crust the members, the government would not be pleased with this sort of withdrawal from society, especially when the renegades can be so dangerous. And when the members came from lower ranks, it would be regarded as even more dangerous, however unreasonable, and the laws propagated according.
And if all four existed, they would have different laws for dealing with them.