While it is generally agreed that the folkloric figures of "Link" and "Princess Zelda" are based on real historical individuals, neither those individuals nor their respective myth-cycles were contemporary, being separated in time by nearly two hundred years, with each initially being the protagonist of their own body of tales.
When the two myth-cycles were fused by later chroniclers to produce the combined Link-Zelda cycle which is familiar to audiences today, the figure of Link assumed the role of overall protagonist. Securing Zelda's freedom from captivity is often inserted as a secondary objective into episodes which were originally Link tales, while Link typically subsumes most or all of Zelda's role in episodes which were originally Zelda tales.
In many cases, the Link-Zelda version is the only iteration of a given episode which survives, so determining which tales were originally part of which precursor cycle is not without controversy; however, the repetitive nature of the perils which preclude Zelda's active participation in many episodes – kidnapped, possessed, sealed in enchanted crystal, etc. – may offer some clues.
(The Gamelon saga represents the the largest known body of Zelda tales which are believed to have persisted in more or less their original form. Linguistic analysis suggests that the episode in which Link is revealed to have been trapped in a heretofore-unmentioned magic mirror the entire time is a clumsy interpolation by a later author, inserted to justify the saga's inclusion in the broader Link-Zelda cycle.)
The very first Legend of Zelda was itself a Zelda legend, hence its title. It was also one of the first to be adapted to the contemporary Link-Zelda structure of the myths. The introduction of Link into this myth was shoddy and introduced a number of inconsistencies.
For example, it's said that Link is a wanderer from afar who rescues Impa from Moblins but when he arrives in Hyrule, he has to take the place of the unarmed and inexperienced Princess Zelda. And so this allegedly experienced warrior who just killed a bunch of Moblins arrives in Hyrule without so much as a sword in hand.
Similarly, the original myth featured Zelda assembling the Triforce of Wisdom, the only force that could stand against the Triforce of Power in Ganon's possession. Because it was the first to be adapted, there were concerns about disempowering Zelda by replacing her entirely with Link. As a result, a strange compromise was struck; One in which Zelda, after assembling the Triforce, then immediately broke it back down into its component pieces and re-hid them for Link to find.
By contrast, The Adventure of Link, true to its name, is the first Link legend. The importing of Zelda into it as the sleeping princess that Link awakens from her long slumber proved to be just as clunky as the importing of Link into The Legend of Zelda. Most notably, the confusing questions raised as to whether Zelda is meant to be the princess Link rescued in his previous adventure or the one he is rescuing in this new one.
Similarly, Zelda's nemesis Ganon is roped into Adventure of Link very awkwardly. Link's nemesis is his own dark shadow, with only a scant few mentions of the idea that Link's defeat will somehow result in Ganon returning... just because.
But the largest and most consequential of adaptations made to The Adventure of Link is the revising of the magic scepter Link uses to awaken the Sleeping Princess into the Triforce of Courage, a modern invention meant to tie Link more closely to Zelda and Ganon's mythos.
And this is where the study of the legends' history becomes rocky, as many scholars consider the very notion that the Triforce of Courage did not exist in the original tales to be downright apocryphal.
We also can see the shoehorning of Zelda into Link's Oracle Saga, where instead of having 2 unrelated adventures, Ganon's minions form a superficial bridge between the two stories to introduce peril to Zelda - Zelda's presence or lack thereof has no significant impact on either story
And there are some distinct quirks to the Gamelon cycle that argue for the presence of syncretic merging of the Zelda in the tales we know with a similar legend from another culture. As does the difference between the Triforce of Wisdom, her sometimes status as a Sage, and the Sacred Power/Light Force/etc power that has different names in different legends.
But it's an interesting pairing of a Celestial legend (Zelda) with a Cthonic one (Link) - after all, how many of the stories that clearly are originally Link tales involve another world? I submit as evidence the presence of stories such as Link to the Past and Majora's Mask; even in the Era of Twlight cycle, we see a previous version of Link resurrected as a shade.
On the flip side, the Era of the Sky gives us Zelda as explicitly, canonically a reincarnation of the Goddess Hylia; whether this was part of the original mythos, or an evolution of why she has the Sacred Power of light in her bloodline is unclear to me. But Skyward Sword was clearly, originally, a Zelda story - after all, Link spends the entire tale chasing after Zelda.
Skyward Sword cannot possibly have been a Zelda tale, because it clearly follows the ur-pattern of the Legend of Link, wherein Link meets three challenges (usually associated with the colors green, red, and blue) and is rewarded with his principal sword, with which he is then able to meet some number of additional challenges before defeating his foe.* However, it is highly likely that in the original iteration, it was Hylia and not Zelda whom Link sought. Skyward Sword has many hallmarks of being a later expression of the Link cycle, including themes of enlightenment and spiritual transcendence that are very different from the simple physical violence of the earlier expressions. Link's quest for Hylia is a quest for the essence of divinity itself.
Current research seems to indicate that the oldest extant version of the Link tale is the one labeled Wind Waker, which clearly dates to the Hylians' Seafaring/Exploration period, before they settled in the land which they named Hyrule (the legend-within-a-legend wherein Hyrule is sunk under the sea can be attributed to a later admixture of elements from other versions of the Link cycle, or other mythologies entirely). There is of course a Zelda figure in Wind Waker, but for the first half of the tale she is identified as Tetra, a very different character indeed! There is speculation that most of the "Zeldas" in confirmed Link stories were actually Tetra, his original female companion, before she was overwritten as Zelda when the two mythologies were merged.
* Linguistic scholars believe "Ganon" to derive from the Hylian root dialect word gann, which simply translates as "enemy" or "opposition." There is no reason to suppose that every instance of "Ganon" or "Ganondorf" in the tales refers to the same entity!
While identifying Tetra with Zelda is of course the product of later revision, the revelation that Tetra is herself a princess may not be.
As previously noted, descent into a mystical Underworld – often, but not always, explicitly identified with the realm of the dead – is a common element of Link tales. This descent is frequently paired with an encounter and subsequent rivalry or alliance (often one, then the other) with that realm's queen. In particular, the motif of Link forming an early alliance with a mysterious young woman who later proves to be the Underworld realm's queen-in-exile is not found only here; consider, for example, the (admittedly divisive) Twilight saga. Indeed, if we accept the identification of the Skyward saga's desolate surface realm with such an Underworld, the revelation of Link's childhood sweetheart as a mortal incarnation of the goddess Hylia arguably fits this mould!
(Of course, as the earliest versions of the Wind Waker saga are presently lost, any conclusions regarding exactly how this trope was introduced to the tale are unavoidably speculative. In the absence of further discoveries, whether Tetra was originally simply a young pirate lord who acquired her Underworld-queen attributes in the process of being fused with Zelda, or whether she was already queen-in-exile of a very different Underworld which was later replaced with a fallen Hyrule to justify her identification with Zelda must remain an open question.)
This sort of discussion often implies an air of disdain for later additions and alterations to the "original" myths (whatever "purer" version of them the writer has in their head), but there's plenty of compelling historical value to be found in such changes, even apparently minor ones!
For example, Tingale of Limpa might by now have been known only for his contributions to cartography, were it not for the comic character based on him (and on a general caricature of the aristocratic unemployed of the time) becoming so popular among theatre-goers that he became a stock character in plays decades after his death, and that The Masks of Majora coincidentally became so iconic a retelling as to preserve the character as a vestigial piece of reference humor far beyond its original context. Of course it's not a coincidence that this version of the character manages to be tied well to the themes of the play and the Mask myth before it, so we must give credit to the playwright. Still, the fact that a noted writer could include such a character at all speaks to the general tensions the nobility had with the lower orders of society at the time, and their growing displacement by the rising merchant class.
Obviously, the increasing sway of the nouveau riche is much more directly apparent in the character of Beedle, who was created because Beidwen Delmor insisted on being able to get a minor stage cameo in every play written under his financial patronage, if he felt like it.
