The words "Narrative" and "Story" are often used interchangeably, but they are not synonymous.
A Narrative is a set of event-types and ideas, typically related and selected for thematic purposes but not necessarily sequential nor dramatic. It is open-ended. Narratives involve theme, order, word choice and emphasis, but exist without any need for Plot. A Narrative does not need a Structure; it just is. Entire cultures can (and do) tell themselves Narratives. The Theory of Evolution is a Narrative. "Land of the Free, Home of the Brave" is a Narrative.
A Narrative functions as both a Template by which Stories are interpreted, and as a Filter determining which Stories will be accepted and which will be rejected or denied by adherents of that particular Narrative.
A Story is more directly tied to the concept of Plot and Character. It is a set of events with a Beginning, Middle and End, selected and arranged so as to convey a particular Meaning and/or Point of View. A Story, when it "works" (i.e. in a manner many people find acceptably resonant with one Narrative Structure or another) is the manifestation of a Narrative, in such a way as to support or refute it.
A Narrative Structure (like that shown in the image above) is the shape and purpose of a Story, absent the mundane, non-archetypal details. A Narrative Structure can be emergent, but if it's done right, what it emerges "into" is an already-existing (because archetypal) Narrative Structure, in either its positive (affirming) or negative (denying) form. To make matters slightly more confusing, a Story's Structure is called a "Narrative Structure" when we are speaking of the framework or formula rather than the content. That's because we're looking at a template. Joseph Campbell's famous "monomyth" is a Narrative Structure. So is Aristotle's dramatic arc.
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The Difference between Narrative and Story is part of a structuralist approach to game design and interactive storytelling currently being explored by the As If Collective. These principles are at the root of the "ScenePlay" narrative card game system, currently in playtesting. Join our Patreon Community to follow and contribute to this project.