Another possible distinction.
Some say that "traditional" is not so much to do with authorship or written-oral distinctions per se, but rather that a song exists within a community's traditional culture.
It is something of the past that they hang onto and cherish because it's of the past. What kind of community? Well, I suppose, for a start, one that's been round long enough to develop traditions. This would probably also apply to the way a song is sung and when and where.
The problem with this really is how to define a 'community' I suppose - do any and all connections between people, even fairly impersonal ones like listening to somebody's record, join you to a community?