The way that spirits work is that something with starch or sugar is fermented, and then that fermented product is distilled. And due to the way that distillation works, and the specific equipment and techniques used, the resulting distillate has some of the characteristics of the original fermented product. So rum has distinct sugar cane/molasses flavors and aromas. Whiskey has flavors and aromas from the specific grains that are used to produce it, brandy has flavors and aromas from grapes (or whatever fruit is used).
On top of that, many spirits are aged in wooden barrels, which may or may not be charred, or have been used for other products. Bourbon is aged in new charred oak barrels, Scotch and rum are aged in just about anything- sherry (a type of wine) barrels, port barrels, old bourbon barrels, and so on. All of which donate a little flavor and aroma of their own, while removing other, harsher flavors and aromas.
That said, distillers can get tight enough on their distillation to pretty much get straight ethanol and water out of their stills, regardless of the fermented product going in. That’s why you see vodka made from so many different things- various grains, corn, grapes, sugarcane, and so on. In order not to be whiskey (various grains, corn), brandy (grapes) or rum(sugarcane), they effectively have to distill it to the point where you can’t even tell what it started with.
Some products such as gin, are made from neutral spirits (i.e. spirits , but infused with botanical ingredients specificallly to impart specific flavors and aromas.
But the big question at that point of disti is why bother? Just get the cheapest grain neutral spirits you can, and have at it. There’s no point in getting anything else if all you’re looking for is to get a buzz and mask the flavor of the alcohol with something flavorful.
Most people though, like the interplay between ingredients and spirits as found in highballs, cocktails and other mixed drinks, so they buy whiskey, rum, vodka, gin, etc…