Well, 'narrative' is another word for story. It's often used to describe a sequence of events or a tale.
How about 'tale'? It usually refers to a fictional or traditional story, often with elements of magic or adventure. Like 'A fairy tale' or 'An old folk tale'.
Another option is 'protracted story'. It implies that the story goes on for a considerable time. You might also hear 'drawn-out account' used in a similar way.
Main character. A story usually revolves around the main character. This could be a person, an animal, or even an inanimate object in some cases. In 'The Little Prince', the little prince is the main character. He is the focus of the story, and all the events and interactions are related to him in some way.
Romance. It is a very common alternative word for love story. Romance often implies a relationship filled with love, passion, and sometimes adventure.
Resolution. This word implies the solution or outcome of the various conflicts and situations presented throughout the story. It's like when all the problems and mysteries in the story are finally dealt with, and we reach the end. For example, in a detective story, the resolution is when the detective reveals who the criminal is and how the crime was committed.
A common alternative word for a horror story is 'scary tale'.
Another word for a short story might be 'fable'. Fables are often short, have a moral lesson, and can be considered a type of short story.
Prehistory is another word for back story. It refers to the events or circumstances that happened before the main part of a story.