Is it superWoman or Supergirl

Answer 1

It depends on who you are referring to. If you mean Superman's cousin Kara Zor-El, then you are talking about Supergirl. She came to Earth as a teenager. Since Superman grew up here, he was her mentor.

You could say that since Superman was Superboy in his youth (well in some incarnations) she could have grown into the name of Superwoman, except that ... well ... something else happened to her first (for details, see Crisis on Infinite Earths).

That was the easy part. Now for the hard part.

Back in the "Golden Age" of comics, there were a lot of superheroes with familiar code names, but civilian identities and backstories that were completely different from those that would come later in the "Silver Age". For example, there was a Green Lantern, but he wasn't Hal Jordan and he didn't get his ring from a dying alien, he was Alan Scott and his ring was a magic artifact (and one-of-a-kind; he wasn't part of a Green Lantern Corps).

Most importantly for this discussion, there was a Flash. He wore blue pants and a red shirt, had no mask, and wore a silver hat with wings on the sides (a lot like the one the guy in the FTD logo wears). His name was Jay Garrick. When later writers recreated the Flash in the form of Barry Allen, they decided that his choice of the name (and some aspects of his costume, like the little wings on the sides of his head) were influenced by growing up reading about the adventures of Jay Garrick, the Flash, in comic books. One day he was messing around with the sort of semi-sciency stuff the Silver Age Flash used to get up to, and somehow managed to vibrate himself into a parallel universe where Jay Garrick was real. The two had an adventure together before Barry vibrated back to his own universe.

Cute little story, nice wink at older fans. And readers loved it. So there was a rash of stories where the modern Silver Age heroes somehow managed to get from "Earth-1" (the universe where the current stories were taking place) to "Earth-2" (the universe with the Golden Age heroes) and meet up with their own counterparts.

Superman and Batman existed in both the Silver Age and Golden Age and were very similar, so they met sorta-themselves, except that Superman-2 had married Lois Lane while Superman-1 was still single, and so on. They were also older than the Earth-1 versions (Robin-2 was no longer the "Boy Wonder" but a grown man, for example, and had given up the short-shorts for a more respectable outfit).

The crossover stories were wildly popular. So someone decided ... if there are two parallel universes, why not three? And Earth-3 was created, but with a twist: The heroes of Earth-1 had villainous counterparts on Earth-3, and while Earth-1 had the Justice League and Earth-2 had the Justice Society, their counterparts on Earth-3 had formed the Crime Syndicate. There was one superhero on Earth-3: Alexander Luthor (yes, Lex Luthor was a superhero), who was kind of an extremely high-tech version of Batman (and married to Lois Lane).

Superman's counterpart was Ultraman, Batman's was Owlman. And now we get to the point of this whole long digression: the Earth-3 counterpart of Wonder Woman was ... Superwoman.

Earth-2 also had their own Supergirl. She now lives in the mainstream universe (Why? Read "Infinity Crisis".) She goes by the name Power Girl. And that's what happened to thatSupergirl.

The 1985 mega-crossover Crisis on Infinite Earths was supposed to consolidate all the various universes into one single continuity (in the process of doing so, it killed off Supergirl-1; sorry for the spoiler, but seeing as how the "Pieta" cover of Crisis #7 is such an iconic image, it's hard to imagine anyone who might care didn't already know). The single-universe idea didn't last, though; since then, the Superman/Batman comic has visited a sex-reversed universe, where the counterpart of Superman is Laurel Kent aka Superwoman (and the counterpart of Supergirl, Laurel's cousin, is "Superlad").

Answer 2

Supergirl is the teenage cousin of Superman, while Superwoman is an alternate version of Lois Lane from a parallel universe where she gains superpowers. Both characters have different origins, powers, and storylines in the DC Comics universe.