First, we shall take into account that speaking about deity (or deities) we only hope to understand a little, and that there’s plenty of interpretations of what, at the end, we can’t fully understand, prove or deny with absolute certainty anything.
Most of the ancient people that inhabited Europe were polytheist, as many others around the world (like the American inhabitants, for example) that kind of polytheism take into account personal and independent deities, with different characteristics, they may have a common genealogy, but equal status, comparable powers and even they tend to fight each other.
These entities were very local and they pick some people and tribes in their protection, and some ask for some forms of henotheism, that certain tribes only address to them, or mainly address to them. So there were cities, tribes and even nations dedicated to the veneration of one god or goddesses as their patron. We have just to remember the war of troy to see an example.
As time passes, these concepts were merging with a concept of one God (or Goddess) superior to the others, most of the times, they tend to refer to the top on the genealogy and give that attribute to the Father God or the Mother Goddess, as the king or queen of them all, with enough power to control every other god, and even attributes of creator of both, man and gods. That happened long before Christianity arises, so it was a natural evolution in pagan societies and philosophy.
The Celts were not the exception, and we can find that at different stages there was a king of Gods, or leader, that receive special veneration, as well as a Mother Goddess.
How ever, the speed on which the Mediterranean Pagans (Greeks, Romans, Egyptians, etc) merge to the idea of one God above all others, without question, was slower in the evolution of the religion of the Celts. But then, the invasions take place. First the Vikings, then the Romans, after that the Saxons, etc. and that obviously change in a certain way the cosmology of the Celtic people of the Islands, France and Spain.
But still, there are basic differences between the Mediterranean, Nordic and Celtic pantheon. One of the most significant is that the Celtic Gods are not limited to one mainly attribute, as for example, Mars God of War, Apollo God of the Sun, Athena, Goddess of the wisdom, or Aphrodite Goddess of Beauty. When first approaching the Celtic pantheon, as we have as reference the Greco-Roman pantheon learned in the schools, we tend to ask “who has the god of war for the Celts?” but there’s no answer to that, because there are various gods and goddesses associated to war, and battles, and the sun, etc.
Of course there are main attributes, and as in other religions as the Hindu and Egyptian, there were figures that merge in triads, with triple Celtic Gods and Goddesses.
Another great difference is that Celtic people view the Gods as their ancestors, they were all descendents of the mix between the Gods and the Men, the Thuatha dé Dannan and the Milesians, for example, and not created by them with only special characters know as demigods, as Heracles.
But even with the influence that invasions, commerce, etc give, one thing remains, every god has its individual and independent characteristics, personality and were separate entities. Even if the acknowledge of one above the others, one almighty and creator, their sons were creations but not parts of him/her, as we are different from our own parents.
Christianity take this concept from the beginning and early Christians had a pantheon of angels, demons and saints to address in specific occasions, all created by One God, even if that god take the form of a trinity, remains as an inseparable entity, and also separated of the other saints and angels, and of course of the demons, that were originally also angels.
Catholic, Orthodox and Anglican Churches today still keep that idea, meanwhile most of the Protestant Churches, some sects of Judaism and Islam, see this as a form of polytheism (which in my opinion it is) that has to be avoid.
But then, as time passes with the advent of the Christians and Christianity spread over Europe, there was a merging, as all we know, between the ancient gods/goddesses and the Christian Saints. But there was one figure that originates a new concept. Mary, the Virgin.
And this is a important entity, since in the form of Mary, many pagan Goddesses were put into the Catholic faith, usually the Mother Goddess, as Danna, Minerva or Coathlicue (in America) but, how the Catholic Church explain that they were all but the same, Mary, the mother of Jesus the Christ? Simply, they include a philosophical idea that it was risen by that times, no matter how many virgins there are, and their different attributes, they are all but different faces or manifestation of one, “the Mother of us all”.
When time passes, and the revival of pagan faiths, now know as neo-pagans, begin; that concept was introduced and extrapolate to the Gods also, so, the statement that “"All gods are one God, and all goddesses are one Goddess, and there is one Initiator” emerge. How ever is my understanding that the first published book that use that sentence is by the Sea Priestess by Dion Fortune, and it has been taken as a part of the teology of many pagan religions.
This concept is know as soft polytheism, where at the end all merge to just one male and one female principle, and all others but manifestation of that. Then, some neopagan faiths keep that concept and extrapolate it to One single entity, the Uncreated, The One, that has the male and female attributes merge in one.
Under this concept, even if we address to different names of gods and goddesses, we are addressing but to one (or two) entities, and just appealing to one of its (their) qualities.
My personal view is stick to the hard polytheism, but in its later form, I mean, I believe in The One, the creator, beyond and above all other gods, but independent of them, and the other gods, or powerful spirits of the universe (that’s my name for them) as independent entities, with their own area of influence, powers, characteristics, behaviour, and personality, never as faces of one single (or dual) entity.
Now, came the problems and questions. Myths talk about the relationship between this deities, and their areas of influence, as an example, Isis interact with the gods of mount Olympus, as well as Epona enter the Roman pantheon. Now we have another gods in other parts of the world, in America, in the near East and the far East, etc. How they interact? Is it okay to address to some in the area of the other?
I think, that some may have different names but are the same in different cultures, but others, shall be independent and local, how can we know the difference?
Well, these are my two pence about Hard vs Soft polytheism.