The readings that GUEST (20 Oct) gives are the ones in the standard edition of Burns (Kinsley).

Kinsley dates this version 1784-1785.It's titled "Green grow the Rashes. A Fragment".

Kinsley also prints from 1786 a less-respectable "A Fragment". The chorus -- "Green grow etc." -- is identical to the Merry Muses version, but the three stanzas are different.

Burns (leave aside the ambiguity of how much the songs are his, and how much doctored versions of songs he collected)often did both respectable and less-respectable versions, but I'm not sure what the authority of the Merry Muses texts is -- I'd be a bit wary.

But Burns' song is totally independent of "Green grow the rushes [sic], O"

There are [at least] 6 related British versions of this (one from Scotland!) written down in the nineteenth century. The one which has the two lily white boys all dressed in green comes from Dorset.

The next related song is "The Dilly Song" which begins similarly, but begins to diverge at verse 4:

Four it is the Dilly hour
When blooms the Gilly flower
Five it is the Dilly bird
That's seldom seen but heard

The American versions usually begin "Come and I will sing to you" -- linked to "Green grow the rushes, O" but not identical.

Some of this (and a lot more, including various guesses at who the lily white boys were) is in GREEN GROW THE RUSHES (COMMENTARY), but some isn't.

Robin