It's a completely different song, though Gardiner may well have found a "blue" rather than "yellow" variant; or Kennedy may have got it wrong, which isn't unheard-of. That particular set hasn't ever been published, at any rate.

Bonny Blue Handkerchief (as posted by Stewie) was a popular song in its time, and issued by a lot of 19th century broadside printers. There are a number of examples at Bodleian Library Broadside Ballads:

Bonny Blue Handkerchief

Number 378 in the Roud Folk Song Index, and found in tradition mostly in England, though it has turned up in Scotland and Ulster; and a recording of a set from California (1941) can be heard at Voices from the Dustbowl:

Page with a link to it.

Did "Aengus" credit their source? I assume they are, or were, an Irish or Irish-style band. The only Irish sets I know of are in Sam Henry's Songs of the People, but it isn't either of those.