In the sense that narrative often has a relatively clear plot-line and a "story", then it is different from poetry, I guess. But that tells us nothing in and of itself about what that story means. If I was to say that the Odyessey was about this bloke wandering through the Mediteranean for ten years, that would be true; but it wouldn't tell us much about the meaning and purpose of the stories.
The interpretation, i.e. what the author meant (what God meant through the human author), is a concrete thing,
It's also, sadly, quite unknowable. We can gather a certain amount of evidence to say what we think the author's meaning might be; we may even get reasonably close to it. But, to take the letters of St Paul: was he writing for us, in the 21st Century? No he wasn't; he was dealing with particular problems in particular churches, some of which we can piece together from the clues in St Paul's letters. Issues such as eating meat offered to idols and the judaisers are not ones of direct relevance to us, and we only pick up little bits about this from the text. But they are all part of St paul's intended meaning; and we only know a certain amount about the issue.
The other thing, of course, is the unintended meaning of a text. When I write a poem, or anything, I have an idea about what I am trying to say; but other people reading it bring their own experience to bear on it and read it from a different angle. Sometimes other peoples' ideas of what I meant are actually of interest to me; because they show me things in the text that I didn't know were there. Instead of rejecting them, I take them on board, unless they have completely misunderstood; in which case, it's either my fault for being unclear or their fault for being thick.
When we speak, we mean something specific.
Well, no we don't always. Sometimes, we're not clear about things ourselves. A lot of my replies on this board are not neccessarily neatly-formed ideas; they're more like workings-out; and a lot of conversation is like that. We work out what we think as we go along. I suspect that the letters of St Paul are more like workings-out than clear, logically-ordered arguments, for instance. Also, of course, the poets of the Bible (and there are a lot of them; even the "histories" are written in poetic form) are not putting forward arguments as such. Many of the Psalms are hymns or laments directed at God, not at a human audience; they are cries from the heart, not an argument intended to persuade. The same is true in a different way of the prophecies: it's doubtful that the authors were always clear about what they were saying, because they were working through ideas and probably emotions that were strange even to them.
That's why I say that it's not so much that there is a clear, unequivocal single meaning for every passage; but more that there is a "field" of meanings. This is where, I'm afraid, your own theological position comes in. Christians have been fighting for centuries over the "correct" interpretation of scripture; people have died over the interpretation of one or two scriptures.
It's not that there aren't wrong meanings; and that wrong meanings would probably be totally unconnected to what we know of the original intention of a text. But the question of what is the right one is more difficult than saying "my church reads it this way therefore we're right you're wrong." A lot of church doctrines are not clearly readable from scripture, including the Trinity, for instance. So it becomes a question of authority: who's authority do you trust to give you the "correct" interpretation? The Church of Rome? Pastor Smith?