I wonder if it is considered as plagiarism, if 2 heroes from 2 different movies have the same power or such.
For example, Storm from Marvel X-Men is well-known by her powers to control weather and so on. Let's say, if studio ABC makes a new movie, features "Laura" with the same powers like Storm's, more or less, will Marvel sue them for stealing their "fictional superpowers". Just curious.
Plagarism... NO.
Plagiarism is using someone else's work without giving proper credit.
Copyright infringement... Possibly.
Copyright infringement is using someone else's work without getting that person's permission. The author of any original work, including books, essays, Web pages, songs, pictures, and videos, automatically gets the copyright to that work, even if she doesn't label it with the copyright symbol and her name.
The issue is that "powers" are usually generic (run fast, really strong, control weather, shrinking, getting really large, etc.) or based on existing myths. Unless the character is actually being copied (with perhaps a name change) it's unlikely that a suit would succeed.
That said, such things are vetted during production for legal conflicts and the production company would have looked into these things ahead of time.
If something was likely to cause a conflict then usually representations would be made, probably in the form of a "Cease and Desist" letter putting the offender on notice.
Actually suing is expensive and the only people who really win are the lawyers.
DC & Marvel have "competing" characters going back decades and this has rarely led to actual legal action.
Of course, with "movie money" now at stake... that might change.
According to Wikipedia there was a
...Second Circuit trilogy of 20th century copyright infringement cases in which the proprietors of Superman copyrights sued other companies for publishing fictional exploits of a cape-wearing superhero.
(Believe it or not) the first two were successful, but the third was not:
