There is no reason why a word cannot have different meanings in different contexts. It is absolutely fine for "traditional" to mean one thing in the world of classical music, another in jazz, and another in folk - indeed, you would expect it to. As long as you use the terms correctly in the appropriate context, there should be no misunderstanding.

The problem we seem to have in the folk world is that we don't seem to be able to agree what it means. Everyone has their own interpretation, and seems determined to stick to it no matter what anyone else says. Perhaps I'm as guilty of this as anyone else, although I like to think that my interpretation has a logic to it and makes a distinction which is relevant and significant.

Traditional songs aren't necessarily out of copyright. The famous example is Ewan McColl's "Shoals of Herring" which was apparently found circulating in the tradition as "Shores of Erin".