I think the differences come the variables associated with the composition of an individual barrel as well as how different barrels are stored. One barrel might have more slightly more char. Another might be slightly more absorbent. Another might be stored closer to air circulation. Etc. Etc.
Anyway, those all produce different notes in the same fluid, even if only subtly so.
So if you take all of those barrels and you pour them all into the same vat, the nuanced differences from the barrels' individual variables get muted. I'm making this next part up for the sake of illustration.
Say you have 3 full barrels, each comprised of 10 parts of fluid.
- Barrel A has 4 parts "oakiness", 1 part "sweetness", and 5 parts generic.
- Barrel B has 2 parts oak, 3 parts sweetness, and 5 parts generic.
- Barrel B has 2 parts oak, 1 parts sweetness, and 7 parts generic.
Now you combine all 3. From all 30 parts, you're going to have 8 parts oak, 5 parts sweet, and 17 parts generic. That's 27% oak, 17% sweet, and 56% generic. That might be an exceptional mix. Regardless, it'll taste different from Barrel A, which by itself was 40% oak, or Barrel B, which was 30% sweet.
So you can go and taste Barrels A, B, and C, and whichever you like best, maybe it becomes your "barrel pick", and you get the bottles, through a sticker on there, and people snap it up because it's notably oakier or sweeter or whatever compared to the standard bottle.
Sometimes, a particular batch or barrel will develop a reputation, and then people will hunt it out since that information sometimes shows up on the sticker. "Oh, the batch that was on floor 12, section J of the warehouse is EXCEPTIONAL" or whatever and then the price goes haywire.