The general term "fiction" is a form of art or entertainment that is largely derived from imagination, although it may be based on real events. Specifically, "prose fiction" as a form of literature is the more artful of the two. "Hills Like White Elephants" is, therefore, a work of art. It has been canonized as a "classic" short story and included in a larger body of work (in this case, anthologies that continue to be taught in schools).
My favorite working definition of "fiction" is that is ironically "true," oftentimes truer than reality. It is an author's perfect assembly of lies that paradoxically lead an audience toward the truth. Various schools of philosophy have challenged this point:
The sociological school of constructivism argues that every view of reality is fundamentally a construction of the self and that a safe distinction between fact and fiction is impossible, whereas the philosophy of naturalism holds that reality can be approximated and truth can be demonstrated through usefulness, allowing the distinction from fiction.
So, what makes it artful fiction, instead of fiction of entertainment? In this story, it's use of metaphor and authorial voice. Hemingway uses setting to parallel the topic of discussion. Hills are symbols, metaphors for the female--in this case, her womb.
Hemingway is known for his plain, tough style of narration. Few quotation marks, dialogue tags. Lots of subtext. What's not said in this story is more important than what's said. Hence, the title. The topic of conversation, though never explicitly stated, is as big and looming as those hills.
Artful prose fiction can also be read from many angles. Literary critics can comment on this story from various schools: Marxist; feminists; archtypal; psychoanalytic; etc... But I think the best judge, in the end, is the average reader (like yourself) who "believes" this story to be true.