Even establishing "historical facts" is trickier than it seems (how do you know King George actually said X? — the chain of documentation is often trickier than one realizes until one actually starts to look into it), but yes, the goal of history isn't just finding said "facts," it is selecting the salient ones and stringing them into a narrative that tells us something (the interpretation/argument). The narrative might be saying, "this is why this war began" or "this is why this party took power," but there's always a this is why or this is how sort of thing at the end.

Historians are a type of storyteller, for sure, although the methods, goals, professional positions, and so on are much more specific when you say someone is a "historian." If you say "someone is a storyteller" it doesn't tell you what kinds of stories they tell, whether there is methodological rigor to their story construction, whether they care about whether the story is true or false, whether they are trained in figuring out what makes a fact "true" or not, etc. When you say someone is a historian, you are implying a degree of specificity to the types of stories they are writing.

Storytelling requires a narrative logic, some understanding of how to move from one story beat (something that happens) to another in a way that will be comprehensible or interesting to the audience. This is also how the construction of a logical argument works: given what we start with (our assumptions and our evidence) which kinds of inferences are valid, and which are not? Which rules of transformation are allowed and which are not is a question of method, which goes back to epistemology - how do we know what we know? But everyone has to accept some ways of knowing, and reject others, if only in an informal or ad hoc way. Just as different audiences may find particular ways of storytelling compelling or confusing, depending on their own background, so too do historians coming from different philosophical, ideological and methodological backgrounds find particular kinds of arguments compelling or not. Just because a narrative is widely believed, or is very believable from a certain point of view, doesn't mean it is true, just that it followed a particular set of rules closely enough to resonate with an audience that subscribes to those rules. A logical argument is, in that sense, just another form of rhetoric, albeit a damned useful one, appealing only to people who believe in its rules.

Historians generally agree on the importance of preserving the details of evidence to ensure that the narrative at least does not contradict the evidence. This is not an ironclad rule, as sometimes the evidence itself can be shown to be the problem - it is biased, it means something different than we thought, it was forged, and so on. But clinging closely to this rule and only assembling a narrative using clearly demonstrable facts is quite boring - the historian-as-chronicler - and even then is not immune to bias. One can assemble a deeply misleading story using only clear, reliable evidence by putting the facts in a particular order, or leaving out inconvenient facts, or guiding the reader towards inferences that do not really follow from the evidence.

No historian is in command of all the evidence, let alone all its possible interpretations, and if it might be uncontroversial to claim things that can be examined directly ("The US constitution begins with 'We the people,' and you can tell because we have copies you can look at...") the questions we are usually interested in do not so obviously match with what is directly evidenced in the documents ("The US constitution was an ambiguous compromise between pro-slavery and anti-slavery elements in early American society." Maybe true, maybe not, but we can't just read the document and find out, because it involves motive, context, multiple parties, and so on.)

And so, historians also build narratives in terms of broader interpretations, related not to the direct facts, but to bigger ideas about how the world works. These ideas can be drawn from other disciplines - sociology, economics, political science, or even biology or physics. There is then somewhat of a two-way interaction between historical narrative and bigger theory. Historical facts can be used in tandem with theory to build a larger narrative: for instance, a Marxist interpretation of the French Revolution will involve combining Marxist ideas about how societies and economies work with the evidence of the French Revolution to try and make some greater sense of the whole event, to help us understand the "why" behind the "who, what, where and when." But historical facts can also be used to call these theories into question, to show that the theories must be flawed or incomplete because they do not fit well with the historical evidence. Both modes are important types of narrative (argument) that are built in history, but one is more obviously "storytelling" and the other more a critical method for evaluating stories.

There are some scholars elsewhere in the social sciences who have also picked up ideas of causal inference as being a form of narrative, or at least narrative having a place in more technical systems of inference, for instance Andrew Gelman and Thomas Basbøll (2014) "When Do Stories Work? Evidence and Illustration in the Social Sciences." So even for hardcore Bayesian number crunchers, the work they do can be seen as just a very mathematical form of argument, which is itself a kind of storytelling, putting one thing after another in a way that tries to make some sort of causal sense of it all.