Sorry, I can see that you're not trying to attack. There are, however, a fair number of people here who seem to be mocking or denigrating or refusing to believe there is or should be a difference.

Ah, style. It's not about the style of playing. A traditional song played by a rock band still sounds, to me, like a traditional song. A modern song played on a solo bagpipe still sounds modern. It is only about style if you're including the actual composition in the definition of style. And, maybe even more so, the lyrics.

Listen to Steeleye Span (not the stuff they wrote themselves - most of it doesn't sound particularly traditional to me) and then listen to U2. Can you hear the differences in the construction of the melodies and in the nature of and words used in the lyrics?

Listen to Martin Carthy's traditional material and then listen to Joni Mitchell. Can you hear the compositional and lyrical differences?

Where did the songs come from? That is probably the easiest way to draw a line if you need one. My own line is a mile wide and isn't black, but many shades of gray. Did the musician write the song or did they interpret a really old song? If they wrote the song, can they play it in a set of really old music without having it stick out like a sore thumb? That's a pretty simplistic difference, but it's a place to start.