I have been trying, unsuccessfully, for some time now to get educationscotland.gov.uk to either remove or rewrite their page on Auld Lang Syne as it is misleading and confusing for the children at which it is aimed. I won't quote the whole article but it says that Burns, because he had already used the air for O Can Ye Labour Lea, Young Man, he used another tune ".... he called The Miller's Wedding and that is the tune we use today".
The "tune we use today" or the one known throughout the world, is note for note O Can Ye Labour Lea, Young Man. The Miller's Wedding/Daughter is more like Coming Through The Rye but has echoes of O CYLL,YM but the well known melody, it is not.
Modern academics may have just taken Francis Collinson, page 6, Traditional and national Music Defined, as gospel when he printed an air called The Miller's Wedding, which was actually OCYLL,YM and subtitled it Auld lang Syne.

I agree with Jack that Eddie Reader's version is dreadful. I don't think she understands some of the words and sings "freer" for "fiere".