Mike, 32 gallons was the size of the English ale barrel - ale as opposed to beer. The beer barrel was 36 gallons.
In the early 1800's before Imperial measure was adopted, the U.S. and British measures were the same, i.e. an English pint was 16 ounces as still in the U.S. (it's 20 now in the U.K.). So these old measures sound to me the same as what they would have been in England, allowing for the regional disparity there Imperial measure obviated.
Why a full barrel in Pennsylvania is just under 32 gallons is hard to understand, a half barrel was the expected 16 gallons, so I'm not sure about that, but the connection to England is still evident.
Many here, but not all, will know that ale differed from beer in that ale originally was unhopped. Beer was always hopped and came in to England from Flanders it appears in the 1400's. Once all ale became hopped, the distinction lost its former importance and the term beer and ale became used in a way that was often hard to distinguish or rationalize.