For some time I've been following a company called Shakers which makes vodka in the U.S. This company came out of the team that produced Pete's Wicked Ale which until sale of the brand was a successful, pioneering micro-beer. Shakers is making a splash around the country. Pat Couteaux is the company's distiller and has advanced degrees in distillation science. Pat Couteaux has been interviewed numerous times about his company's product. See e.g. www.cocktailtimes.com, also www.findarticles.com. He states that the grain from which vodka is derived and the mix of grains affects flavour and mouth feel. He classifies flavour as neutral if corn is used, "soft" if wheat is used and spicy if rye is used (he speaks of a "hint" of spice from the rye). He describes in detail the complex distillation process - 6 distillations - used by Shakers to get what it wants in the flavour profile. I am not an expert on vodka, much less chemistry, far from it, but he is focusing on grain source as a differentiator here. On the company's website, www.shakersvodka.com, it is claimed the taste "embodies" the wheat the vodka is made from. It is suggested the further removal of congeners, in two final extractive distillations, allows the wheat character to come through.
There would appear to be different views of what constitutes a lack of taste. I am not saying I could detect these differences on a blind taste test but then again I rarely drink vodka. I recall having some Stoli recently at a Russian-style restaurant and it struck me as "empty", lacking body and flavour. But then too my regular tipples are some of the most flavourous whiskies made, so it is going from one extreme to another..
Also, I would note each maker of GNS (as legally defined for proof level of course) establishes its own specification for its brand. There is no national standard which specifies what residual congeners can or cannot be in the ethanol or in what percentage. No doubt distillation to 190 or 192 proof in pratice will remove most congeners that affect flavour - most but not all because otherwise why would some distillers continue to rectify pure alcohol? Shakers' site makes clear that its first four distillations removes the water from the spirit. The last two are intended to remove congeners that (presumably) don't deliver the taste profile the company is looking for. If in fact the "wheat" still influences the final product there must be something in the spirit derived from the wheat that delivers this result - I assume this consists of very small amounts of "good" congeners that help impart the taste desired. I was reading of a vodka made in France and sold in the U.S. - can't recall the name at present - that is distilled from wine. It is sold here as a "vodka" (thus meeting the legal test Chuck has mentioned). The taste notes given indicate a scent of white grapes. Byrn writing in the 1870's noted that no matter how much a grape brandy from lees (kernels and skins of grapes left over from winemaking rehydrated for fermentation) is distilled, it still shows some character from the source material (the typical grappa flavour is what he had in mind). I can only assume that something must remain in the ethanol no matter how prolonged the distillations and filtrations to explain such results.