So, there's a philosophical question that underlies this issue. Most gods in polytheistic systems are identified with one or more natural or social forces. There is some profitable work to be done in talking about earth gods across cultures, because the earth is a concrete thing we can observe and talk about. (This is the approach Socrates seems to hint at in the Apology.) So to an extent, I would say, yes, the Sun is the Sun, and different cultures ascribe different theological, literary, or symbolic value to it.

But you seem to be asking a more specific question with regard to the relationship between Celtic and Greek myth. And there is a historical relationship there: both Celts and Greeks share elements of what is called Indo-European culture, which originally spread from a place we don't know for certain (but debate constantly; in any event, most definitely NOT Sumer) west all the way to Ireland and east to India, and then a few millennia later spread further still due to colonialism. Language, culture, and religion across this massive stretch of land all share at least some common roots.

So in certain cases, we can very definitely identify similarities. *Dyēws is often regarded as the chief god of the Indo-European pantheon, related to the concept of divinity itself, *deiwos. (A * before a word indicates that we have reconstructed that word etymologically). There are many local deities that use one or the other of these names, often with the word for father (pitr, pater, etc.) appended. In India, this god became marginal and is known as Dyauṣpitṛ (द्यौष्पितृ). In Greece, we find the form Zeus (Ζεύς/Δεύ). In Latin culture we find Jupiter (Deus/Father) or Deus, variants (Dios, Dieu) of which are probably still the most commonly used term for the divine today... including the word "divine" itself!

Beyond this, ancient authors tried very hard to come up with commonalities, as most succinctly expressed in the interpretatio graeca/romana. It doesn't seem to me that you're pointing at this here, but I am aware that Julius Caesar at least expressed interest in trying to uncover the identities/Roman names of Celtic gods worshiped in Gaul. (Do check that link out if you have any interest in this topic; it's a really interesting read and the translation is good.)

All that said, I can't speak as an expert on Irish mythology per se. (Could answer with more authority on other parts of the Indo-European world though, if that is helpful.) My amateur understanding is that, for instance, the term referred to above (*Dyēws) is used in Irish as a term for divinity (día), and may have some measure of connection to one or more gods particularly. In general, language will be most persistent, specific gods less so, and mythology less still. I would be fairly surprised to find strong mythological links between Irish and Greek myth. Perhaps someone with a more specific understanding of Irish mythology could say more.

Further (free!) reading: https://archive.org/details/189942876InSearchOfTheIndoEuropeansJPMallory

It’s rare I can answer a question on r/AskHistorians, let alone two in twenty-four hours, but I think I have some useful knowledge here. I’m going to start with a disclaimer that I’m not a trained anthropologist and can’t speak in detail to the contemporary anthropological view of the question of shared origins between pagan religions. However, I can give some literary history that explains where Graves got this idea and what it’s doing in works like The White Goddess.

The "all gods are one" idea saw its full flowering in James Frazer's The Golden Bough (1890). The Golden Bough is ostensibly a study in comparative religion. It argues essentially that all cultures have similar stories in which a sun god marries an earth goddess, dies, and is reincarnated.

Frazer was a man of his time, and thus was influenced by various strains of thought in the late Victorian period. In The Literary Impact of The Golden Bough, John B. Vickery argues that Frazer was attempting to use a scientific lens (a la Darwin) to study religion, while also being influenced by Victorian religious thought.

This kind of alternative religious thought was very much in vogue in the late nineteenth century, in part due to the destabilization of traditional Christianity by Darwin's theory of evolution. Groups like the Theosophical Society and the Hermetic Order of the Golden Dawn claimed that they had access to an ancient, global spiritual tradition that drew on the ancient wisdom of all cultures. These groups also drew on what we now recognize as pseudo history and pseudo archaeology that claim all cultures spring from one super advanced, master culture. The best example of this idea is probably Ignatius L. Donnelly's Atlantis: The Antediluvian World (1882), which was adopted and promoted by the Theosophical Society.

In other words, there was something in the air in the late nineteenth century that made people think that a global monoculture made sense. It’s origins are complex, but Frazer breathed it in and wrote a book applying the idea to religion.

At the same time, there was a literary movement in Ireland known as the Celtic Revival, championed by the poet W.B. Yeats and Lady Augusta Gregory. Most of us today know Yeats for his post-World War I poem "The Second Coming," but in his early career, he and Lady Gregory attempted to reconstruct Celtic myths. Lady Gregory in fact collected a volume of Irish folklore, trying to rediscover an authentic Celtic heritage beneath the Anglicization of Ireland. Yeats wrote many poems and plays that drew on Irish mythology, such as The Wanderings of Oisin, Cathleen ni Houlihan, and At Hawk's Well. It should be emphasized that these writings were reconstructions and revivals, because we simply don’t have access to pure, unadulterated Irish myths. As Yeats's career progressed, he drew on other mythic traditions, searching for something more authentic. He was involved in both the Theosophical Society and the Order of the Golden Dawn, and became interested in Eastern religion and this idea of a global ancient religion.

My understanding is that, from an anthropological perspective, Frazer and Yeats have never really been fully accepted, but both were quite influential in literature. Other writers took up Frazer's methods, looking for a transcultural myth or religion. Other examples include Jessie L. Weston's From Ritual to Romance (1920), which argues that medieval romances (ie, King Arthur stories) are directly descended from pagan religions, and Joseph Campbell's The Hero with a Thousand Faces (1949). A lot of people are likely to be familiar with Campbell's monomyth because George Lucas consciously used the story structure to write Star Wars, and he’s hardly the only one to have done so.

This brings us back to Robert Graves, who loved The Golden Bough and used it as an influence in The White Goddess—combined with the Celtic Revival influences of Yeats, much in the way that Lucas used Campbell to write Star Wars. The White Goddess reflects ideas about cultural diffusion and one single origin point of all human ideas.

If you’re interested in this topic, you might want to pick up a copy of The Golden Bough from your library and page through it to see where Graves was getting his ideas from. The original is loooooong, so you’ll want to find an abridgment, which will also be long. I like the Oxford World Classics edition, personally. John B. Vickerey's The Literary Impact of The Golden Bough is a pretty thorough treatment of how Frazer influenced writers, but I recommend it with the caveat that he treats Frazer's work pretty uncritically, so read it with the fact that The Golden Bough is not accepted history/anthropology in mind.

"myths" is a tricky one since it requires a certain model of religion. In effect that you know your gods through stories about them. Not everyone uses that approach (the Roman adopted it from the greeks).

Celtic religion is poorly attested to put it mildly. We don't really have any first hand accounts and even second hand accounts are limited. Julius Caesar compares some Celtic gods to Roman gods and Pliny the elder mentions some religious practices involving oak trees. Archaeological evidence and alters produced under Roman occupation provide evidence of which gods were worshipped but again no real information on any myths.

Barry Cunliffe's Iron Age Communities In Britain has a fairly short section on this but then there isn't much to say (although he has a lot more to say about burrial practices).

There are a few surviving welsh tales and christianised tales that look like they might be Celtic in origin (they feature cut off talking heads a lot) but those don't have much in common with Greek myth and are too small a sample size to draw much in the way of conclusions from.

Would you say that Celtic myths being Greek in origin is a) bollocks, b) possible although not likely, c) something we have some evidence for maybe, or d) actual fact? how far is that a thing for other ancient people's and pantheons?

They could both be considered branches of the Proto-Indo-European religion. However the link to Celtic religion is based on the name of deities and their roles rather than myths. Its possible that the Celts had some myths with some common origin with Greek myths but that would be speculation. Iff they did those myths would come from the Proto-Indo-European homeland. There are various candidates for where that was but Samaria isn't a candidate I've ever seen.

tl;dr: The specific statement that "Celtic myths and deities were Greek in origin" is wrong. I should preface this by saying that the following statements are not based on history, but on the study and philosophy of religion. If there are good historical reasons to believe that specifically Celtic gods were described based on knowledge of specifically Greek gods, I'm not aware of it.

Any culture's myths and deities are culturally bound, and arise in that particular culture. Comparisons between deities (for example and most easily comparing and contrasting Roman to Greek gods) are at their core comparing and contrasting different belief systems. Different beliefs give rise to different gods, and similar ones give rise to similar gods.

To look for a common origin for gods, our best bet is to look at the mystic tradition in various different religions. In the philosophy of religion and study of religions, we have progressed beyond statements like "All mystical experience can be divided into a small class of 'types' which cut across cultural boundaries. Though the language used by mystics to describe their experience is culturally bound, their experience is not." (from Katz, taking a contrary position)

Again in Katz we're drawn back to the idea that people in different belief systems have different expectations of what will happen during a mystic experience, and this expectation shapes mystic experiences in important ways.

(i.e. There are very similar descriptions of the mystic experience between Christian, Jewish, and Islamic mystics, for example, who all describe "Unity with God". But whereas the Christian mystic describes "Unity with God", identifying a singular creator deity as expected by his belief system, a Buddhist mystic describes how he "experiences Nirvana", and native american mystics describe how "experiences how everything has life".)

From my own perspective, I think it's a small step to say that the mere fact that human beings are having these various religious experiences in the context of various faiths shows a deep similarity between religions that goes beyond a statement like "the Celtic gods are actually Greek gods" - which if I understand Graves correctly, he is basing on descriptions of the gods' roles - which might very well be similar, but similarity does not prove descent.

You might be interested in Prothero's God is Not One, which is a critique of this perspective. He is not writing as an historian, but rightly points out that this view is relatively recent, modern view, and presents the potential issues. More generally, this is not a widely used approach among scholars of religious studies today, which has largely shifted to a comparative perspective that does not assume similarities a priori. Prothero reflects this shift. (As another example, the World Religions text book by Partridge et al. makes this point in a less polemical way than Prothero.)