The ancient Greeks used both words and appeared to have originated both. The first form appears first in 517BC by Hecateus of Milietus. The word is still known in the 12th century AD where it's used in the Alexiad to describe Franks. The word is supposedly from a Celtic word referring to themselves.
Galatai though is taken (by modern linguists) to be from a Celtic word 'galos' and was used to describe the Celts who invaded Anatolia. The state of Galatia later named for them. No mention of where the t came from though.
The Greeks used the two terms indiscriminately so my question is whether these words could have come from the same original word? I'm not a linguist and what I've seen so far doesn't address these words together but as separate things.