So who are the original 'Celts' anyway,if the Celtic speakers are excluded? And how are the peoples of Ireland and Britain,not Celts then?
Celts ("companions", "allied", possibly) were probably, originally, a confederation/coalition of Gaulish peoples in southern Gaul based on economical and possibly political grounds that traded and interacred with Phoceans of Massalia : initially Greeks named local "Lyges" or Ligurians (basically the "noisy people") and called Celtikè the region they interacted with and evetually Celtikoi their people.
Celtic ensemble came to include more and more regions in Gaul : it's unclear if "Galatians" was an endonym for Gaulish people or only a regional name, but with the extension of Celtikè to most of Gaul things got mixed up. Then in the IIIrd century, Belgae formed a new sub-region in Nothern Gaul (out of transrhenan and danubian migrations westwards), while people along the Channel formed another one ("Aremorica", meaning "the Coast") due to a distinct percieved ancestry while still being included in pan-Gallic ensemble. Celtic Gaul became then again a distinct region of Gaul and remained it so until Caesar.
The idea that all peoples related in language and using same cultural (Halstattian and LaTenian, at least for the Iron Age) proceeded from a same civilization appeared in the XIXth, when historical romantism played fully particularily with a certain "celtomania" (Ossian, for instance). And giving they were not given a specific name, "Celt" was borrowed and assumed being the name for all of this.
What we call Celts is vastly different from what Romans, Greeks and Gaul considered "Celt" themselves.
Not that you didn't have a sense of kinship beyond the regional cultures : especially, Gauls acknowledged a relation with Brittons (especially Belgae settled there but not only) and Germani (which were various peoples, a mix of Germanic, Celto-Germanic or even Celtic peoples) whom the name itself is probably a translation of a Gaulish word for "relatives". But they didn't considered them as Gauls either.
The original Celts were referred to by Greek authors as living in what is now southern France. If I remember right, Caesar referred to the inhabitants of Britain as "Britons", not Celts.
Caesar had to make some actual ethnography there, instead of heavily relying on Poseidonios.
Basically Britton is related to Brittanai (possibly being a Gaulish word for this place and peoples originally), rather than a local ethnic/political name, and originally named the population of the whole British Isles, not just Britain then but also Ireland. Listen, it was far, it was cold, they were tired, they called it a day. And before Caesar, that was it except a geographical differenciation between people of Ierne/Ibernia and Albio/Albion was made.
And the future dictator was confronted with a tiny bit more complex reality. First, Belgians were settled in Britain there too, and formed distinct people and ensemble. Then it appears that a significant part of Brittons are really, really closer linguistically and culturally to Gauls even without considering Belgae, in spite of associating Brittons with Gaels as you still sometimes see (which is at least heavily debatable IMO) and that part of Northern Britain's peoples while related to them closer than with Hibernians, might form a distinct enough ensemble. We don't know much about these people regional organisation, but the possibility of regional coalitions under the form of patron people or high-kingship is there with, for example, Cassivellaunos or
Togidumnos; and the possibility of a distinct southern British ensemble comparable to Celtica or Aremorica
So, while Caesar used "Brittons" to name the whole population, he as well acknowledged we we're talking something more complex than this and doesn't use Britton other than a geographical consideration, while noticing there were insulat Belgae, people closer to Gauls than other Brittons, and the other sort of Britton.