Stories set in the historical past include histories AND historical fiction, which proves "fiction or non-fiction" is an unhelpful distinction. To suggest more helpful categories, let's try "foreground or background".
Story worlds set in the "present day" easily evoke readers' extensive awareness of their own present world. In most fiction and journalism, as well as much that is memoir and contemporary biography, the narrator can frequently, easily, and confidently refer to ubiquitous facts, terms, locations, contexts, customs, and practices which need no explanation. Whether fiction or non-fiction, then, stories set in the recent past (or "specious present") can devote nearly all their attention to foregrounded material, usually without working hard to evoke much "background" at all.
In contrast, story worlds set in the past must evoke audience knowledge that is sketchy or second-hand. Whatever audiences think they know about "the past" may derive from personal, social, collective and/or cultural memory but that "knowledge" will surely be evoked with all the distortion, uncertainty, and vagueries of mnemonic awareness. Narrative representations of famous figures and well known events must construct their historical background by evoking familiar and sometimes unfamiliar aspects of history, which means some stories therefore work harder than others to establish just how a foregrounded storyline relates to the background of history.
In short, background evokes things the reader already (thinks that she) knows, and foreground informs the reader about developments previously unknown. And, just to reiterate, these dynamics affect any story situated in the historical past, whether fiction or non-fiction.
Now, what's really interesting is how differently these two basic functions can be applied.
In his contribution to Reading Historical Fiction (2013), Hamish Dalley suggested a working taxonomy with two types of Hist-Fic storytelling, focusing on the historical status of the protagonist in terms of personal agency. To illustrate using popular movies, one type is like Cameron's Titanic and another is like Spielberg's Lincoln. That is, one type keeps historical material predominantly in the background, while the other foregrounds historical figures as protagonists.
In Titanic, the protagonists' power to affect their own lives (in the foregrounded narrative) does not extend as far as altering the famous event (the historical background), which - we know from the outset - is going to dominate that movie's basic plot. The story is therefore focused about how Jack and Rose react to the boat sinking. Background and foreground interact at key points, but remain mostly separate, running parallel for most of the storyline.
That's a very different relationship between background and foreground than we find in Lincoln, in which the protagonists themselves are historical figures whose personal agency works to bring about the famous events, which - we know from the outset - are going to bring about the story's denouement. Because foreground and background are more fully integrated, the story focuses on illustrating and explaining how that ending comes to pass, and what else happened along the way.
Note: Dalley noted this probably isn't a full taxonomy, and I won't try to expand it myself in this space, but it might be fun to sketch a punnet square on foreground/background, and evocation/information. A third division might regard fact & fiction. Are there any kinds of storytelling where the whole background is both non-historical and built largely by exposition? Sci-fi and counterfactual histories come to mind. Or what about foregrounds that stick entirely to well known points of historical fact while the background (remember, not the back-story, but the period-setting) is fictionalized? I'd have to imagine something like Shakespeare's Julius Caesar set on Jor-el's Krypton. But, now I have severely digressed...
Dalley's two categories provide a working taxonomy for stories set in the past. He applied it to literary works of historical fiction, but the same principles hold for non-fiction, despite considerations of historicity. For a quick proof case, I could tell you the story of how my grandfather was captured in the Battle of the Bulge (1943). In telling that story, the relationship between foreground and background would clearly parallel the case of Titanic, rather than Lincoln, and yet the story is completely non-fiction. For the other category, while most proper works of history are easily distinguished by incorporating substantial stretches of analysis (authorial exposition), it's just as obvious that historians routinely ascribe agency to the major figures in their non-fiction literary portrayals.
The point by now should be clear. Whether fiction or non-fiction, stories set in the past can be categorized based on the way they construct a relationship between foreground and background.
To wrap up today, let's connect this with New Testament studies.
Whether fiction or non-fiction, Matthew 2 is like Titanic. We know Herod dies and Archelaus takes over. We know Galilee is going to be split off from Judea and handed over to Herod Antipas. We know Jesus will be safe there. Because we already know all this stuff (or we should, because a first century Judean audience absolutely would have known these major events from their own recent history before hearing the Gospel according to Matthew) the writer is focused on forming connections, explaining how his protagonists (Joseph & Mary) reacted to these famous events and were affected by them. For another example, we might consider the episodes where Jesus stands before Pilate, in which Jesus' pending fate has caught up with him so completely that his agency as a character (actually, if not potentially) has effectively disappeared.
Other episodes in the Gospels, whether fiction or non-fiction, are more like Lincoln. The early christian audience already knew Jesus was going to be crucified at the end of the story. What's shocking is the idea that Jesus embraced this fate early on, and that Peter was initially against it. Likewise, we already know Jesus is going to rise from the dead. That's why the original (shorter) ending of Mark could get away with 'cutting out' at the end. The resurrection could be referred to "off stage" (so to speak) because it was thereby evoked in the audience's memories of oral tradition; so the style of that evocation enabled the type of poetic effect that the writer was aiming to create, but the fact that a writer could rely on the substance of that evocation is what made such a literary gambit viable in the first place.
These are just a few thoughts about foreground and background as a more helpful tool for analyzing the Gospels - not as fiction or non-fiction, but - as stories set in the past.
There may be much more worth considering about this...
Note: For an acknowledgement of narratology's traditional lack of attention to non-fiction or "historical" narrative, see p.380-81 in the Routledge Encyclopedia of Narrative Theory.