Sorry it took so long to answer this.
Within modern Celtic archaeology there are two opposing camps; Celticist, who see the aforementioned linguistic-archaeological cultural continuum, and anti-Celticists (like myself) who prefer to see a more complex pattern. In truth there are a variety of cultural differences which lead us to think that the "Celts" were not nearly as uniform as previously theorised. One of the first to be identified is the fact that house styles differed considerably. In temperate continental Europe (except for a few isolated finds in Normandy which appear to be the result of British immigrants) people inhabited rectilinear houes, the same is also true for Celtiberia. However in Britain (except for late 1st century BC and 1st century AD south east Britain), north western Iberia and, we think, Ireland, people lived in round houses. The round house and rectilinear house pattern has is a continuation of Bronze Age traditions and predates the Hallstatt and La Tene cultures which we associate with the Celts.
The cultual continuum is also not as uniform as it may appear. The Celtiberians did not make use of the La Tene style, except for a few imports from Gaul, and neither did southern Ireland or Galatia. The Britons, although usually classified as being part of the La Tene world, had a variant of La Tene which is unique enough to warrant it being ascribed its own typological sequence. Nor can we, with certainty, link the British style to the continental style and its developments. Also, within the continental style we find variations, most notably in Hungary where a regionalised style known as Dragon La Tene exists. The Gauls around Robertesque and in Bohemia produced stone sculptures whilst those else where produced wooden sculptures, or in some case no sculptures at all. Also a supposed cultural continuum doesn't explain why some Celts adopted coinage and some did not. Nor does it explain why those Celts who adopted coinage based their coinage on different Mediterranean models; the Belgae based their coinage on Tarentine and the Macedonian coinage of Phillip II, those east of the Rhine used the coinage of Alexander the Great, the Celtiberians used Roman and Punic coinage as the basis of their issues whilst the Arverni used Rhodian, Massaliote and Macedonian coinage. The Britons adopted Belgic coinage but then changed it so much that the later issues bear no similarity to the original Belgic coins. Likewise with the adoption of writing, the Gauls adopted the Greek alphabet, the Celtiberians used the Iberian and then the Latin script whilst some Britons used the Latin script whilst the Irish developed their own script, ogham.
It is also theorised that, until about c.200 BC, the phrase "Celt" was not commonplace among Celtic peoples. As a result of mercenary service in the Mediterranean and Near East and contact with Mediterranean societies who used the term, Celt was adopted by more people in Iberia and temperate Europe as a means of identifying themselves. However, until the 18th century, no-one in Britain or Ireland (except possibly the Belgae and Parisii) referred to themselves as Celts.
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