Vodka is almost universally manufactured from the same high-grade industrial ethanol, which is essentially pure. However, you are correct that some of them taste different! You might be disappointed, though, to discover that these flavors are often introduced as a small quantity of concentrates added to industrial ethanol during the bottling process. Not every brand has a subtle character modifier added to it but many do.

I know the family that owns the bottling plant for most of the vodka brands sold in California, from premium to bum brands; they bottle everything from the same railroad tanker cars of ethanol from ADM. It was eye-opening to see but it makes sense; ethanol distillation is a highly refined, industrial scale process. Ironically, some of the cheapest stuff is the purest (it costs money to add adulterants to ethanol, after all). The industrial distillation columns are extremely efficient, so extra "distillations" don't buy much.