For someone like me, it's often fairly obvious what is or could be "trad" and a song or tune can be researched. More generally, I might also describe a tune as "traditional" if it was written by a known composer in what seems to be that idiom. That's a personal thing, of course, and not technically or legally correct.

However, as this discussion shows, the main issue here seems to be that of "arrangements" and "adapted" versions as opposed to the original songs or tunes which have been handed down over many years.

When we pick up a song or tune in a session somewhere or just absorb it "omosis style", we are not necessarily aware if one or more notes/words are part of "So and So's" copyright arrangement. I don't necessarily play it the same way anyway and, not infrequently, if I continually play a tune(same applies to singers and songs)it can often change through time consciously or otherwise. Sometimes, what I play might be a hybrid of different styles including my own but I wouldn't dream of claiming such as my own arrangement for copyright purposes. However, many so called "arrangements" in books are little different from what is universally played with the exception of the odd note here and there.
To me, this seems just as naughty as performing or recording a tune without crediting the copyright holder.

Luckily, I enjoy this music as a hobby and don't have to worry so much about recording or live performance(At least in terms of public concerts) issues. I have been involved in both to a very limited extent but matters of copyright etc have always been someone else's worry.