If you take a tenor banjo, tune it GDAE, and proceed to play a bunch of fiddle tunes like Old Joe Clark, Cripple Creek, Big Scioty, Arkansas Traveler, Stone's Rag, June Apple, Billy in the Lowground, Chinese Breakdown, Old Molly Hare and so on...are you still playing "Irish" tenor banjo or could what you are doing be considered Old Time tenor banjo?
And, further more, if when not playing the lead melody you employ chording and backup techniques that would be perfectly acceptable for a mandolin player but do so on tenor banjo, are you doing it "wrong" (as this sort of backup on tenor banjo in Irish music is perceived), or would that be permissable? Chording on tenor banjo is certainly OK if what you're doing is considered New Orleans Jazz