Only a few Grey Cock variants have any supernatural element; those that do probably had it grafted on from versions of The Lover's Ghost, though scholars differ on that.  I'm with Sandy on this one; this example is clearly James Harris/ Demon Lover/ Housecarpenter, and I'd also mention that The Suffolk Miracle is another, completely different song.  I'd guess that RVW was referring to alternative titles that he'd come across, as I can't see him confusing the songs themselves; don't have time to check references just now, though, so perhaps he did.