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Dirty little secret is, just like the majority of whiskeys in the US are made by one distillery, most imported vodkas start as tankers of ETOH and it's simply what they cut it with that makes the difference.
Well, as for US whiskey, not so much; it used to be 14, with all the recent construction it's creeping up to 20 major distilleries. As you can see from the volume chart, the largest producing distilleries are Jack Daniel's in Lynchburg and Heaven Hill in Louisville; Beam achieves second place using two distilleries, in Clermont and Boston, KY.
Imported vodka, like Grey Goose (France) or Stoli (Russia/Latvia) is blended and bottled in the country of origin unless it states something else on the bottle. TTB rules about labeling are quite specific.
Smirnoff and other cheaper foreign-sounding vodkas like Wolfschmidt, however, are actually locally made, including in the US.
And most vodka made in the U.S. comes indeed from grain neutral spirit (GNS) made by one of three producers: Archer Daniels Midland (ADM), Midwest Grain Products (MGP), or Grain Processing Corporation (GPC), whose distilleries are in Illinois, Kansas/Indiana, and Iowa. Because that's where the grain is.
And because distilling up to the 95% ABV (190 proof) required by law for vodka is hard with a small still, most "craft distillers" buy that stuff too, and just run it through their still again, so they can legally claim they distilled it and charge "craft" prices, like Tito's Vodka; "made in Texas" my patootie.