Roud lists both the English and Irish songs under the same number, but they do seem to be unrelated. Roy Palmer (Rambling Soldier, 1977, 81) remarked that "the phrase 'Hungry Army' was virtually proverbial in the nineteenth century." Unsurprising that there should be two or more songs with that title.

One American song (noted in Indiana) of this name in Roud: Brewster, Southern Folklore Quarterly (1940) p.179, beginning "I wear a medal, as you see". That might be worth a look.

On the whole, copying Peter Kennedy's very abbreviated references here is a bad idea (unless they are suitably expanded). Very few people will understand them, and those who do can find them for themselves. This is not a personal criticism! I've told Joe Offer the same thing several times. I really do think it just confuses people.