As far as MCPS is concerned, every version of a traditional piece registered properly with them constitutes an arrangement, whether an unaccompanied vocal or an orchestration using theremin, church organ and marching pipe band. The skills a singer brings to an unaccompanied song (variation, ornaments, phrasing, pitching, etc.) are subtler in effect than a musical accompaniment, but nonetheless distinctive and worthy of recognition.

But that enables the person registering the arrangement to claim royalties only on in respect of their own performances of that song or tune, and doesn't make it their property as far as anyone else learning it is concerned - it's still in the Public Domain. No-one is obliged to credit the arrangement of the performer they learned it from, although if you copied an instrumental accompaniment note-for-note that would be a different matter morally if not legally. Of course, people can and do choose to credit a piece as "Trad. arr. A. N . Other" if they particularly like A. N. Other's arrangement, wish to copy it and also to give credit where it's due. If, for instance, you were going to sing 'Willie's Lady' to that Breton drinking song melody that most people are familiar with, you could argue that there was a case for crediting it Trad, arr. Ray Fisher. But then, Martin Carthy sings his own Anglicized version of the words so, if you learned it from him, perhaps you should credit his arrangement too. It can get confusing. But the people at MCPS (who include knowledgable folkies) are usually happy to offer advice on grey areas.