It might also mean the highest level or floor in a building in some cases. Say, in a crossword that has a lot of architecture - related words. If the clue is something like 'Top Story in a Skyscraper', then it's about the topmost floor.
Maybe 'epics'. Epics are usually long and complex novels that can be physically heavy due to their length and often come in thick volumes. For example, 'War and Peace' is an epic novel that is quite hefty in terms of page count and physical weight.
It could be 'novella'. A novella is longer than a short story but shorter than a novel, which might fit this crossword clue.
It could be 'yarn'. A yarn is often used to refer to a long, rambling, and perhaps even fictional story.
Another option could be 'parable'. Parables are short stories that convey a religious or moral lesson. While they are generally short, some parables can be more elaborate and thus considered a 'long short story' in relation to the crossword clue. Parables are found in many religious and cultural traditions, like in the Bible for example, and their length and complexity can differ.
Perhaps 'epic'. An epic is a long narrative that often involves many characters, complex plots and sub - plots, and a wide range of events. It can be a story of heroic deeds, like 'The Iliad' or 'The Odyssey' which are classic examples of long, involved stories.
Novel. A novel is a long written story, which is a very common answer for a crossword clue like 'long story'.
Maybe it's something like 'film footage' or 'video capture'.
It could be a word like 'plot' or 'tale'. Those are common terms associated with narratives and stories in crosswords.
It could indicate the headline news. In crosswords, 'top story' is often used to represent the most important news item that would be on the front page and at the top of the newspaper layout.
A clue for a body of fiction could be 'fiction book' or 'imaginary tale'. It really depends on how the crossword setter wants to phrase it. Sometimes they might use a synonym or a more creative description to make it challenging.