It's my understanding that distillation produces alcohol to a very high percentage, over 90%. Obviously this doesn't leave a lot of room for flavour compounds. And indeed a lot of white spirit, such as Vodka, is relatively flavourless.
Some spirits, though, are different. Whiskey made from peated barley retains the smoke flavour of the peat fire, for instance.
Perhaps the most extreme example, though, is rum. White rum has a sweetness compared to vodka which must come from the sugar base. Darker rums, like most aged spirits, gets the majority of their flavour from the barrel in which they are matured. However, tasting darker rums reveals a lot of sugar product flavours: caramel, fudge and treacle for example. Presumably these also come from the sugar base and not the barrel yet they're a lot stronger in dark rum than in light.
Why is this? What governs the flavours that are left behind after distillation and before maturation? Presumably the temperature at which flavour compounds vaporize is key but are there other factors? Is it different for some spirits than for others - would un-matured whiskey, for example, taste much the same as vodka if not peated?