Benhall wrote;
All I can think is that I am, consciously or not, playing with a different embouchure depending on which idiom I happen to be playing, and that these two things just don’t overlap.
Classical music is different from Irish trad (duh, I know, talk about spotting the bleedin’ obvious), no-one would play Strauss’ ‘Wine women and song’ with a reedy Irish tone would they? And you they wouldn’t get away with playing something like ‘Sporting Paddy’ with a pure classical tone.
So yes, I think you could be adjusting subconsciously to suit the style you are playing. 
(edit; forgot quotemarks)