The phrase "a generic story" is correct and usable in written English.
It can be used to describe a narrative that lacks specific details or unique elements, often following common tropes or clichés.
Example: "The movie was entertaining, but it ultimately felt like a generic story that we've seen many times before."
Alternatives: "a typical narrative" or "a standard tale".
The result is a generic story ballet, disappointingly lacking in Balanchine's sharpest choreographic invention.
He said the Web site pages, action figures and virtual characters are an extension of the effort "to put a real face on what has been a generic story about the Army".
As a result it resonates as a generic story, rather than one reported from a war zone.
Even at our own Disrupt conference, Director Joe Green didn't (or couldn't) be interviewed, instead opting for a generic story about the value of immigration reform.
It's a generic story about a generic hero foiling a generic plot hatched by a generic villain, with almost no spice to differentiate the proceedings.
You are not looking for a generic story in these points; rather, this should be a story that fits precisely here and shows something you are trying to display.
In the case of Mr. Lodge's rather mechanical new novel, "Thinks...," it is the old C. P. Snow debate about Two Cultures -- science on one hand, the humanities on the other -- that is supposed to lend ballast and depth to an otherwise generic story of campus adultery set at a fictional British university.
Other issues raised by reviewers included "cluttered screens and annoying 'quests'" noted by GamePro, "over the top" and stereotypical characters opined by Game Informer, a poor and generic story according to IGN and 1UP, and long loading screens and cutscenes which were criticisms brought by G4, 1UP, and the Australian Official Xbox Magazine.
The students were shown two articles: one was a generic news story; the other described a proposed welfare policy.
Though the studio depoliticized most of the film's content, rendering it more or less like a generic adventure story, it resonated with audiences when it was released in 1943, at the height of World War II.
In a sense, it eluded the conventions of a generic crime story (you could safely describe the police presence as largely ceremonial), its emotional centre shifting, rather, with the workings of vexatious marriages, friendships and parental relations.
