I can make maybe a distinction between "Irish trad" and "Irish folk" (though strictly it's a distinction that doesn't really make linguistic sense, since the tradition consists of folk music, whereas the "Irish folk" is largely stuff which arguably isn't ).

But "folk band in the Irish tradition" straddles the distinction. It could mean what yiou want it tomean, which I imagine is why you'd use the term. But one of the things it could mean would be "Irish trad".

Does puffery really get bookings or bring in more punterts? Over and above "this lot are worth hearing" from someone who knows that sort of thing, and is trusted.