A gaul was no more a celt by your reasoning than any other. The first recorded settlement (by the greeks) of celts was north of the Alps. NOT in Gaul. The word Celtus (the roman term for celts) is an ethnic word that is a blanket for all celtic clans stretching from iberia to galatia. The only people you can really get away with calling non celts are iberians (due to punic infulence) and Galatians.
even if the Romans thought celts were just Gauls(which they didn't), why was there an entire word just for Gauls? and another thing, The Romans were stunningly ignorant people. so if they even believed celts were only gauls, id still be looking for another source.
edit: im familiar with the term from the 1700's, but the fact of the matter is, the celts spread from north of the alps, to iberia, to galatia, and then to the isles. the cultures may have changed (which is why you are most likely so confused) but they still shared critical similarities which allowed them to be traced.
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