TAXIING OUT FOR TKOF; A B737 CREW AT ISP BOTH INCORRECTLY THOUGHT THEY WERE CLRED TO RWY 24 AND CROSSED RWY 31 CAUSING A B737 TO GO AROUND.

Narrative

ARRIVED ISP FROM BWI. VISUAL APCH TO RWY 24. DEPARTED ISP TO BWI. ATIS CHANGED DURING PUSHBACK. FO CALLED FOR TAXI. BOTH OF US WERE EXPECTING RWY 24. BOTH OF US THOUGHT WE'D BEEN CLRED TO RWY 24. BEGAN TAXI TO RWY 24. APCHING RWY 33L; I LOOKED BOTH WAYS AND SAW NOTHING. SUN WAS IN MY EYES WHEN I LOOKED R. I HAD MY SEAT SLIGHTLY HIGHER THAN NORMAL TRYING TO KEEP THE SUN OUT OF MY EYES. 1/2 WAY ACROSS RWY 33L; FO LOOKED UP AND TO THE R AND SAID; 'WHAT'S THAT AIRPLANE DOING THERE?' AT THAT POINT A B737-200 PASSED OVERHEAD. I ASKED GND CTL IF WE HAD BEEN CLRED TO CROSS RWY 33L. GND CTL SAID NO. I THEN ASKED WHAT THEY WANTED US TO DO. WE WERE GIVEN A TAXI CLRNC NEITHER OF US UNDERSTOOD. I ASKED FOR THE CLRNC TO BE REPEATED. WE WERE GIVEN A CLRNC TO CONTINUE ON TXWY E; RWY 24; RWY 33R; HOLD SHORT OF RWY 33L. THIS WE DID. WE CHANGED TO TWR. THEY ASKED US TO CALL ISP TWR WHEN WE GOT TO BWI. THIS I DID. HAVING JUST LANDED ON RWY 24; HAVING THE LATEST ATIS GIVING RWY 24; WE WERE EXPECTING RWY 24. MUCH MORE ATTN SHOULD BE PAID TO THE CLRNC. IF THERE IS ANY DOUBT; STOP AND ASK. SUPPLEMENTAL INFO FROM ACN 528566: WHEN I CALLED FOR TAXI I THOUGHT WE WERE TOLD TO TAXI TO RWY 24; WHERE WE HAD JUST LANDED. WE PROCEEDED TO TAXI TO RWY 24 AND AS WE WERE DOING OUR PRETKOF CHKLIST; I PAUSED TO MAKE SURE WE WERE CLR OF THE R SIDE AS WE WERE XING RWY 33L. I SAW AN ACFT COMING IN FOR A LNDG ON RWY 33L. I EXCLAIMED TO THE CAPT; 'WHAT IS THAT ACFT DOING THERE?!' AT THAT POINT I SAW HIM PWRING UP TO GO AROUND. THE CAPT THEN ASKED GND IF WE WERE CLRED TO RWY 24 AND THEY REPLIED NO. WE WERE THEN GIVEN TAXI INSTRUCTIONS TO GET BACK TO RWY 33L.