As I understand it, While Shepherds Watch was one of the first carols that was accepted by the Church, because its words are pretty close to the words in whichever Gospel it is. Earlier carols were tradtitional songs that had no very close connection with church worship, and some of their lyrics were regarded as a bit wide of the mark. Then the Victorians started composing carols specifically for church, and many of the most popular ones date from this time.

So that's why While Shepherds Watched has so many tunes - it was, for a while, one of only a few church carols. And as Ruth Archer says above, there was much more flexibility at that time as to which tune went with whcih song.

Marje