Narrative. A narrative can be a spoken or written account of connected events, just like a story. For instance, a historical narrative tells about events in the past in a story - like way. It often includes characters, a plot, and a setting.
Some other synonyms for a funny story could be 'jocular yarn' or 'droll report'. A 'jocular yarn' is often a long - winded but very entertaining story full of humor. A 'droll report' might be more about reporting something in a really funny and unique way. For example, if you tell a story about a strange event that happened to you in a way that is both unexpected and humorous, it could be called a droll report.
Well, verisimilitudinous fiction can also be considered a synonym. It basically means having the appearance of truth or realism, which is a key aspect of realistic fiction. Another one could be 'naturalistic fiction'. Naturalistic fiction often focuses on the harsher realities of life, just like realistic fiction, but it may have a stronger emphasis on the influence of environment and heredity on characters.
You could say 'narrative' or 'fable' are also synonyms for fiction. A narrative is a story or account of events, and a fable is a short fictional tale often with a moral lesson, similar to some types of fiction.