A mhuire Mhathair was written in the 1700's during the irish struggles against the english and called for Mary's assistance in everyday life. The tune is typically sang slowly.

As Pokarekare was written in the 1900's it uses the irish tune as a basis, I believe a lot of Maori songs written around the time use european folk songs as their tune.

http://folksong.org.nz/pokarekare/index.html has an overview of the origins of the song.