The pre-literate inhabitants of the Balkans possessed an oral tradition not unlike what could be found elsewhere. Stories consisted of various types of legends (stories generally told to be believed) and narratives that were generally understood to be fiction - what we call folktales or fairytales. These stories in their wide spectrum reflected the belief system and culture of the place and time - including rituals and various practices directed at the powerful supernatural beings believed to exist.

Everyone has folklore, and folklore by its nature changes as it diffuses through time and space. At the same time, folktales and legends can demonstrate a certain amount of conservatism, inhibiting change, creating the two forces - conservatism versus change - that tug at oral narratives.

This process also caused regional variation, but on a micro level, difference could even be seen in the context of one storyteller to the next or merely the storyteller and his/her audience who might dispute a detail here or there.

These observations are taken from what folklorists observed in from Europe to India in a pre-modern context, and it is verified by ethnographers internationally. Applying this model to the "prehistory," pre-literate Balkans requires a certain amount of conjecture, but it is not an outlandish reach.

Eventually, people wrote various stories, and the written text could become influential - people have always regarded the written word with a certain amount of deference. Folklore was still capable of change, but now it was tugged in the direction of conservatism by the written word. That said, the various written sources from the Balkans demonstrate a degree of variation, reflecting, no doubt, the variation that existed among people as they told these stories.

Were these "religious texts"? Yes and no. No to the degree that we think of the bible or Qur'an in the context of the past several centuries. Instead, we can think of the texts as reflecting a belief system and associated stories rather than a text that governs those things. And yet, some texts were influential enough to affect practice - again, the respect and conservatism associated with the written word.

Today, folklorists recognize various types of legends. These include etiological narratives that describe how the world came into being in a primordial past; historical legends that describe people and events in a more recent past; and legends about contemporary encounters with the supernatural/extraordinary. These can be seen in ancient Greek texts.

In a modern context, the ancient narratives are often bundled together with the term "myth." That term is problematic in a modern context: it is often applied to "other people's religion," and that is prejudicial. I once had a student who used the term "Indian myths," and I explained that this could be hurtful because there were still people who believed. Indeed, I had a Native American grad student in the class, and she agreed that she would rather not have that term used for her culture's belief system and its stories. Consider, for example, the difference that distinguishes the "Resurrection story" from the "Resurrection myth." Because of this, I reserve "myth" for ancient cultures and avoid using the term in a modern context. This is how I handle the term in my Introduction to Folklore the text I used over the years when I taught folklore classes at the university level:

Something also needs to be said here about myth. People use this term awkwardly. In a European context, myths tend to be the artificial constructs of ancient and Classical-era priests or literate people who sought to weave folk traditions into a comprehensive whole. The exercise often had political purposes, designed to provide diverse people with a single set of beliefs and stories. By reconciling similar traditions, the shared culture of these groups could be seen as more important than the differences, justifying the central rule of the king and his priests. Myth is also a way of organizing and reconciling folk traditions, which by their nature can be contradictory and highly localized. Myth tends, however, to make gods of supernatural beings, giving those powerful entities a status – for modern readers – similar to the Judeo-Christian-Islamic God, even when this comparison is not justified. Of course, it is also important to point out that myths were stories that were told – and then written down – and they were different from religion itself. Many myths were simply the shared cultural inheritance of a group of people.

In general, the word myth is best set aside when discussing more recent folk traditions, recognizing its proper status as a literary genre. Nonetheless, ancient documents recording myths can assist in understanding the history of various stories and beliefs. The authors of these texts were, after all, the first folklorists, and they were the only ones coming close to practicing the craft at the time.

Some folklorists carelessly use the term myth to denote those legends that deal with a fantastic, remote time. This primal era saw the creation of many familiar things such as day and night, fire, animals, people, mountains, and all other aspects of the present world. Folklorists properly refer to these stories as etiological legends explaining the origin of things. Sometimes, however, people interchange etiological legends with the word myth. The problem with this is that “myth” can imply something that is inherently wrong, linked to “primitive” superstitious beliefs. When the term “myth” is used for the folklore of existing cultures or for the traditions that were viable only a generation or more ago, it can take on an insulting, derogatory tone. It is best to reserve the word “myth” for ancient and Classical-era texts.

One of the problems is how myth is usually understood today vs in the ancient period. u/itsallfolklore's answer highlighted and summed up nicely. Yet, not so long ago, the city of Troy was considered pure fiction/just a legend, until it was rediscovered what was left of it in the nineteenth century. In many modern representations, Meriones' gift helmet of boars' tusks (given to Odysseus) is simply nonexistent, but we also have rather recent archaeological finds of Mycenaean boars' tusks helmets... Maybe if our understanding of myth was closest to the past, this kind of discoveries could have happened earlier.

If by generations you also include nowadays, then it is safe to say: quite messy. Of the written legacy: nowadays, most pocket editions or for the general public can come from any edition and author really, it can be difficult to track. If it is based in a critical edition*, then it means that they based the text on a scholar interpretation of different families of manuscripts of a certain ancient work and they very often diverge - if you speak German, modern Greek or studied Latin, you probably know about declensions (if not: sometimes the difference between "I gave roses to Sam" and "I gave Sam's roses" is just a single letter or two), so you can imagine why is important to show where the manuscripts disagree. So sometimes you have two greatly experienced and respectable scholars doing a critical edition of the same work, but sometimes one disagreed choosing A versus B in some parts. The works that chose scholar A will keep the A version and that is what the readers will continue to pass on... And sometimes both A and B are equally valid both in grammar and context. Some people believe that the 'oldest' manuscript is the best to use, but we have evidence that, even during the times of common usage of papyrus and parchment, they had poor copies (with genuine mistakes misreading letters or usage of their modern version of a word) or where they were rather creative when dealing with bookworms' holes with no document to backup the endeavour. It does not help that for a long time they only had capital letters and wrote with little to no punctuation and spaces, let alone when an ancient author decided to republish his work with changes and both editions kept being copied. And all that mess passed to medieval copies... with now including the mess of byzantine Greek intervention in the copying process. But those medieval copies were and are way more preserved and most of our editions are based on them, not papyri. And as mentioned before, those medieval manuscripts sometimes diverge (usually in just a word or two per page). But in general, modern commercial publishers would not bother to point this out.

Yes, there is evidence of regional versions. One example for the Iliad: the Athenian version had the over hundred verses describing Achilles' shield, but the Ephesian version did not have a single one (at least for the generation of Zenodotus, librarian of Alexandria). What happened to Ajax, or Helen, their whereabouts... all that could vary. It is important to point out, however, that their myths were mostly sang/performed (in a common ancient dialect) and marked in their sacred places, and, in a way, was what bounded together places so culturally different like Athens and Sparta. The versions preserved by Roman authors were possibly from different parts of the Greek world or even from within the same city that changed with time. If the ancient Greeks themselves did not have a single united version of the Iliad, how could we expect to have one nowadays?