I've also played jazz - 5 years in a mainstream band plus outings from time to time with other musicians - and the kind of interaction you describe is common (though nothing is quite like the drunken conversations I've heard between two Sunday lunchtime jazz session players over whether such-and-such a chord is a diminished major demented or a minor shredded repented...).

Traditional folk sessions are somewhat different, however, mainly because many of the tunes are indeterminate and with no written harmonic content. If I play, say, "All The Things You Are" in Ab, there's a strong chance that other jazzers at the session will fit in with what I play - if only because the music was formally composed in the first place and the harmonic background is more or less common knowledge. Not the same with many traditional tunes, where a choice of harmonic progression is not so clear. Furthermore, when one "tune" in a session is usually two or three separate tunes played end-to-end, there's not always an opportunity to lay back and meld chords with another chord player. OK if one leads - but no always so easy.