Unless you're downing synthesized lab-grade ethanol, booze always takes in some distinct flavor from the distilling process.
Booze made from sugar, potatoes, corn, barley or fruit will each taste different. Even if the mash is distilled identically. You're never getting pure ethanol by distilling and it will always pick up some flavors from the mash.
Good vodka is finished by further purifying the distilled ethanol through charcoal or limestone. This removes most of the bad tastes picked up during distillation. However, it also gets rid of any character or good taste. Vodka is more like a finely machined tool than a work of art. Once the process is developed, all vodka from that distiller will taste the same
Most brown liquor, like whisky, is finished by aging in barrels. The charcoal inside the barrel slowly filters the ethanol inside as the barrel “breathes” due to weather variations. The flavors from the mash, the charcoal, the wood, the climate, the air, the water, etc ALL combine to give each barrel a unique flavor. Each barrel is like a unique work of art and each distillery has its own secrets that took centuries to perfect.
We sometimes forget this aspect because the big-brand blends use taste experts to blend each batch so it always tastes the same. In reality, each barrel they source from always tastes unique.
Not sure if this was covered, but the minute presence of ‘fusel oils’ (such as propanol and butanol) also greatly influence subtle flavoring of ethanol.