Would anyone know if Amhrán Mhainse / Amhrán Mhuinse / Amhrán Mhuighinse is the same melody as The Rocks of Bawn?

Joe Heaney-The Rocks of Bawn
http://www.youtube.com/watch?v=w8de27O8ILo

Máirtín Seoighe - Amhrán Mhuighinse
http://www.youtube.com/watch?v=V0SLZY2poY8

I found two references (see below) but I'm not sure if they are commonly agreed or educated guesses.

http://mudcat.org/thread.cfm?threadid=147307
Subject: RE: Lyr Req: Identify this song?-Rocks of Bawn
From: GUEST
Date: 12 Nov 13 - 03:48 PM
Tune is same as that of the (in)famous Connemara Gaelic gem, "Amhrán Mhainse" (also Amhrán Mhuinse, Amhrán Mhuighinse).

http://www.irishtune.info/tune/3170/
Rocks of Bawn, The / Amhrán Mhaínse (also as air) (compare melody with melody of Maid from Maraclune #4849)


Thanks,
Amanda