It's said that the word Celt is very problematic as a descriptor for the ancient peoples of Europe. We still use that word because the Romans used that word to describe those people. But "Celt" is too broad to really have much meaning, as those people's all had their own unique cultures. So, are there more regional subdivisions that are more in vogue nowadays?
Hey there, sorry for the very late response but unfortunately I am currently living without internet!!
Yes, the concept of a homogeneous "Celtic culture" is entirely problematic; at their height, Celtic languages were spoken between Ireland and Anatolia, and from Scotland to Northern Italy. Across this vast linguistic continuum, dozens, if not hundreds, of Celtic dialects were spoken by peoples with different social structures, religious beliefs and political organization. Perhaps the only Celtic speaking peoples who called themselves "Celts" were those who inhabited central Gaul, whom Caesar claims called themselves Celts.
There is reason to believe Caesar's claim as most of his ethnographic information seems to be cribbed from a now-lost ethnography on the Gauls written centuries earlier by a Greek historian named Posidonius who seems to have actually lived among the Gauls for a time somewhere north of the Greek trade colony of Massilia (modern day Marseilles). Not only that, but the ethnonym "Celt" itself could possibly have a Celtic etymology, deriving from a Proto-Celtic verb *kel-o- (to hide, cf. Old Irish ceilid) which means "to hide". Ranko Matasovich posits that this very speculative etymology (understandable given the lack of actual documentation) may make reference to Caesar's claim that the Gauls claimed descent from an underworld deity, and that the potential reconstructed name *Keltoy meant something like "descendants of the hidden one".
So there were probably some people who called themselves Celts, at least in a region of Gaul, but as to the rest of them? There is a temptation to equate Celticness with La Tene or Halstatt material cultures, which are the sort of artistic and craft styles most associated with speakers of Celtic languages, however we must remember that an archaeologist's Celt and a linguist's Celt look very different; one did not have to speak a Celtic language to wear a La Tene style sword or a La Tene style brooch and torc, and cultural contact along the Germanic-Celtic continuum proves that individuals belonging to other linguistic groups regularly appropriated "Celtic" styles and designs.
In my opinion, language is the only real defining feature of "Celticness". And among the Celtic languages, there are two competing groupings: Q and P Celtic, which suggests that genetically, the various Celtic dialects split between those which assimilated Proto-Celtic *kw into *p, and those that retained *kw, which developed into q/c in Old Irish for instance. Otherwise, the main genetic grouping of Celtic languages is between Continental and Insular Celtic languages, which argues for a much closer relationship between the Goidelic and Brythonic languages as a consequence of them splitting off from common Celtic. This perspective views the difference between P and Q Celtic as descriptive, rather than genetic (ie. it's definitely a grouping that can be made, but that doesn't mean that it means anything about the relationships between the various languages) and is largely based in an analysis of morphology rather than phonetics.
Essentially the Continental/Insular perspective recognizes that Proto-Celtic and the Continental Celtic languages (Gaulish, Celtiberian, Lusitanian, Galatian etc.) were languages of moderate morphological complexity, resembling Latin, Greek and Sanskrit in their declensional systems (Gaulish is, strangely, grammatically more similar to Latin than Old Irish). Insular Languages like Old Irish, Welsh, Cornish, Breton etc. saw either a complete loss (in the case of the Brythonic family) of case declension, or a reduction of it in Goidelic. At the same time, these insular languages became even more complex than their continental counterparts in other ways, with some mindblowing complification of verbal form (an Old Irish verb has about 120 verbal forms - a modern English verb has about 40) and the use of initial mutation as a grammatical feature of the language that appears to be absent in Continental languages among other similarities.
It goes without saying that I support the Continental/Insular hypothesis as the distinction between Q an P Celtic speakers has lot of holes in it and is based in an analysis of a rather banal sound change that could have occurred independently in the involved languages, or have been the result of sustained contact between Gaul and Britain, which is definitely possible.
So to sum up: the only "Celts" are speakers of Celtic languages, and the only multiregional subdivisions that really hold water are between those who spoke the now-extinct Continental Celtic languages and those who spoke and continue to speak the Insular Celtic languages.
Wow, thank you so much for taking the time to break all of this down for me!