A B737 FLT CREW HAS A RWY INCURSION AT ISP DUE TO A MISUNDERSTANDING OF THE CLRNC.

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WE WERE CLRED TO TAXI OFF OF RWY 6 ONTO TXWY E. BEFORE TURNING OFF RWY 6; WE NOTICED A GULFSTREAM TAXIING TO RWY 24 ON TXWY E. THIS WAS A POTENTIAL 'NOSE TO NOSE' SIT AND WE WERE NOT SURE HOW THE CONFLICT WAS GOING TO BE HANDLED BY GND CTL. WHEN WE TURNED OFF RWY 6 AND CONTACTED GND; THE GULFSTREAM PLT AND GND WERE ALREADY TALKING ABOUT THE POTENTIAL CONFLICT; AND THEN WE WERE TOLD TO STOP IMMEDIATELY AND HOLD SHORT OF TXWY F TO ALLOW THE GULFSTREAM TO PASS. THEN GND CTL TOLD US; 'ONCE CLR OF THE TFC; TAXI TXWY E; HOLD SHORT RWY 33R.' I THOUGHT HE SAID 'HOLD SHORT RWY 33L' AND READ BACK; 'TAXI TXWY E; HOLD SHORT RWY 33L.' THERE WAS NO CORRECTION TO MY READBACK. AS WE APCHED RWY 33R; THE CAPT STARTED TO SLOW AND ASKED; 'ARE WE CLRED TO CROSS RWY 33R?' I RESPONDED; 'YES; HOLD SHORT RWY 33L.' WE CLRED OURSELVES L AND R (THERE WAS NO TFC) AND PROCEEDED ACROSS RWY 33R. ABOUT HALFWAY ACROSS RWY 33R; GND CTL SAID; 'I TOLD YOU TO HOLD SHORT OF RWY 33R.' THE CAPT SAID 'WE MUST HAVE MISUNDERSTOOD; WHAT IS YOUR PHONE NUMBER?' GND CTL GAVE THE NUMBER AND WE TAXIED INTO THE GATE. I THINK THE CONFLICT WITH THE GULFSTREAM MAY HAVE BEEN THE OVERRIDING DISTR IN THIS SIT. THERE CERTAINLY COULD HAVE BEEN MORE COM BTWN TWR AND GND ON THIS SO THAT WE COULD HAVE BEEN TOLD WHAT TO DO APCHING THE END OF THE RWY; RATHER THAN TRYING TO FIGURE IT OUT OURSELVES. THIS WAS A SOURCE OF CONFUSION. FOR MY PART ON CORRECTIVE ACTIONS; WHEN THE CAPT ASKED ME ABOUT THE RWY CLRNC; THE 'LIGHT BULB' SHOULD HAVE GONE OFF IN MY HEAD IMMEDIATELY. THIS WAS A SIGN THAT HE MAY HAVE BEEN UNSURE OF THE CLRNC. THE FACT THAT HE STARTED TO SLOW WAS FURTHER EVIDENCE THAT HE WAS UNSURE. I SHOULD HAVE BEEN MORE PROACTIVE AND JUMPED ON THE RADIO TO CLARIFY. IF I HAD DONE THIS; THERE WOULD NOT HAVE BEEN AN INCURSION. SUPPLEMENTAL INFO FROM ACN 583703: I FEEL THAT I BECAME PREOCCUPIED WITH THE COMS AND INSTRUCTIONS WHILE EXITING THE RWY AFTER LNDG. I SHOULD HAVE CONFIRMED OUR TAXI CLRNC BEFORE XING ANY RWY; AND IN THE FUTURE THAT IS EXACTLY WHAT I WILL DO.