an other thought-- the defination talks of casks-- and the various sizes, including barrel..

but now days, if i saw a wooden container, with straight, or slightly bowed sides, bound with hoops-- i would, no matter what its size, call it a barrel-- barrels are quite common in NY-- our water supply is for the most part, gravity feed, the water pressure is sufficient to get water up 65 to 70 feet (or about 6 floors) Building taller than that all have water barrel on the roof for counter pressure.. Usually these barrels are 500 gallon range.. they are such a common part of the NY skyline most NY don't even think about why the exist..
i never thing of a barrel as a quantity- i think of a barrel as a thing.