I'm one of those that think that trad is basically a static repository. There will be songs that will be found to have an author (so therefore are no longer trad) and there are some songs which are probably trad but have been "claimed". I'm going to ignore tunes, but with respect to songs, trad songs, generally, have a certain style that is missing from modern material. I have been led to believe that trad songs often are written in a mode (eg Mixolydian) that is not fashionable these days. Another difference is that the songs were "written", by and large, so that they could be sung without accompaniment. How does that differ from modern songs? I'll take as an example "Dimming of the Day" (Richard Thompson). At the end of most lines, there are seven beats (just under two bars) left for the accompanying instruments. This is a common pattern in modern songs and this means that it doesn't sound right when sung unaccompanied. However, let's take another Thompson song, "Beeswing". In this song, there are no melodic pauses and could be sung equally well accompanied or unaccompanied. It is this kind of song that although is not trad, could be absorbed as part of a tradition. So I guess I'm saying that although there is a tradition, there is also a body of songs that in style don't just pay homage to the tradition, but could be accepted as part of it. But what I'm not trying to say is that modern songs that do not fall into this style are of less value or importance.
The importance of differentiating between what is traditonal and what is not is not a matter of snobbery. Firstly, there is an historical context. However, in todays' times, it is the ownership and royalties that might have most significance - people's livelihoods could be affected.
That aside, despite my love of traditional material, I'm equally happy to listen to and play contemporary songs/tunes, they both have a value and place. So, I'm not for redefining, but I'm also not for excluding either.