The more dark malt they use, the darker the beer. Flavor nuances come from the specific malts chosen as well as other possible factors, like barrel-aging. Aside from literally looking darker ...

"The best part about barrel-aging any beer is that you get the chance to pull ... bodied" brew with hints of bittersweet chocolate and dark fruit along with a complex, oaky richness imparted ...

Like the difference between lagers and ales (the type of yeast), the difference in taste between light and dark beers (light ... carbonate the beer. Meanwhile, a barrel is just a barrel.