That's a fairly standard form of Willie O, I'd think. The point about the Grey Cock connection is not that Willie O borrowed verses from it, but that a few versions of Grey Cock (mostly from Irish sources) borrowed a verse or two from Willie O. An important distinction; Grey Cock variants with supernatural elements have invariably (or almost so) imported those supernatural elements from other songs.

See Hugh Shields' paper on the subject for full details; I've cited it a number of times in discussions on these songs. The Sweet William's Ghost connection isn't my own idea; it's pretty much the standard opinion, which I follow. Of course there are dissenters, and the suggestion is not that they are the same song; but that the later was a new song based on (or, if you prefer, inspired by) the older.