"Celts" are not a "race" in the modern sense but a culture.

Like "Americans," for example. (Nineteenth and early twentieth century historians and archaeologists often used the word "race" to denote a cultural or national, rather than a genetic, group: e.g., "the Irish race." The word's meaning has narrowed considerably since then.)

The Celts discussed by the Greeks and Romans were united by a common language and other forms of culture (with local variations, of course), no matter what part of Europe they were in.

Think of the English-speaking world today.