There's a distinction I found (in a science fiction novel) that puts "what happened" and "like what happened" in the same general category, and "clearly impossible or unbelievable" in a different category. "Like what happened" would be a realistic novel, or the sort of historical novel that sticks to the known facts and tries to get the historical details right, but adds non-historical characters and lets them talk to known historical figures. The clearly impossible would be stories about time machines, dragons, or Paul Bunyan and Babe the Blue Ox, or a child saying "I didn't take that cookie, Big Bird did."
If you're reading for pleasure rather than information, a first-person narrative of someone talking about his adventures is a kind of thing, whether or not the narrator is telling about their actual life as best they remember it. The line between fiction and nonfiction is sometimes blurred in biography and autobiography, anyhow: we want to be the heroes of our own story, or we don't bother to check the facts, because that fact isn't the point of the story. So someone says "my father died in 1958, when I was 17," and there may not be anyone there to say "wait a minute, you were born in 1942." [I got that example from Samuel Delany's memoir _The Motion of Light in Water_.]