Tentative categories.

EXTINCT: We know there used to be such a song but no one remembers it.

ARCHIVED: We have the words and music but no one sings it any more.

TRADITIONAL: Has been sung for many years(generations?) in a community.

FAMILY TRADITIONAL: Has been sung for many years (generations?) in one family.

FOLK: People sing it now at gatherings.

SPONSORED: Sung only in sponsored groups such as schools, political parties, other organizations, choirs etc..

ENDANGERED: Songs that shouldn't be lost but not many people sing them any more.

PSUEDO-FOLK: The "Sixties" stuff that a lot of people think of as folk.

SINGER/SONGWRITER: Sung by the writer only.

Add your own categories, there must be more. My favorite one is ENDANGERED, I think that folk singers have a duty to sing any song which, in their opinion, should not be forgotten. This duty exists whether or not others consider the song folk.