If I might throw my tuppence in
"Celtic" is a convenient short hand for the Western peoples of Europe - the Galcians, Bretons, Cornish, Irish, Scots and Welsh. Recent DNA studies have suggested a common ancestory that is remarkably old for this area and these people.
The La Tene iron age culture of central Europe encapsulates a very particular artistic and cultural style which is certainly picked up in "Celtic" work of the same period. However, this does not mean that these Western areas were colonised by the La Tene culture people. The evidence is to the contrary and it is now generally considered that the builders of the stone megaliths and burial tombs like Maeshowe and Newgrange went on uninterupted to become the "Celtic" peoples of the Western fringes who traded and interacted with mainland Europe. Irish mythology talks about the Dana coming from Galacia to Ireland and it seems probable that the peoples that settled these areas after the ice age were from very old European stock. Europe was subject to many ravages and movements of people. The Western fringes became the last outpost of La Tene art and culture and many would argue defined it, making it their own.
The term Celts was coined by the ancient Greeks and is unlikely to be a term these people used themselves. The Romans called the Caledonians Picts but records suggest they called themselves the Cruithne or the Prydyn (where Briton comes from)
Least that is my view

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