Jimmy Driftwood wrote the words to "The Battle of New Orleans" that are sung by such as Donnegan to the tune of "The 8th of January." It was Driftwood's biggest hit and has been recorded by many singers since his first record was released. The other song discussed here, I suspect, is not related to the "8th of January" tune other than mentioning that date in the first line. Seems to be one of the "Cruel War is Raging" family of songs.

Sandy (making plain the obvious?)