The tune in Joyce is very similar to the one in DT though it is not identical, even allowing for the fact that it is measured in eighth notes rather than in quarters and is in a different key. But no-one could say they are different tunes. You'll notice that the lyrics in DT are also slightly different from Joyce's, except for the third verse which is quite different. (But we're a long way from The Blackbird And His Mate, I trow).