B737-700 CREW HAD MISUNDERSTOOD ABOUT WHICH RWY THEY WERE CLRED TO LAND ON.

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MISUNDERSTOOD LNDG CLRNC: APCHING ISP FOR LANDING AS THE PNF; I COPIED THE ARRIVAL ATIS AS VFR AT THE FIELD (APPROX 1500 FT BKN; 7 MI) AND UTILIZING THE ILS FOR LNDG RWY 24 AND ALSO; (UNDERSTOOD). LANDING AND DEPARTING 15R. I DECIDED TO MONITOR THE FO'S APCH WITH THE HUD. NEW YORK APCH VECTORED US TO A LEFT DOGLEG INTERCEPT TO THE RWY 24 ILS; SWITCHING US TO ISP TWR AS WE BROKE THROUGH THE 1500 FT BKN CLOUD LAYER AT ABOUT FIVE MILES ON FINAL. I REPORTED TO TWR THAT WE WERE ON HIS FREQ FOR RWY 24 AND RECEIVED HIS CLRNC TO LAND ON ( I BELIEVE) RWY 24. I ACKNOWLEDGED THIS AND REPEATED IT TO THE FO. AT ABOUT 700 FT AGL ISP TWR ASKED US IF WE WERE GOING TO CIRCLE. I WASN'T SURE WHY HE ASKED THIS; I THOUGHT HE WAS POSSIBLY OFFERING A RWY MORE CLOSELY ALIGNED WITH A CHANGING SURFACE WIND; THE FORECAST WINDS WERE GUSTY BUT THE ATIS WINDS WERE STEADY AND LIGHT. I ASKED FOR A WIND CHECK. TWR REPLIED THAT HE HAD AN AIRPLANE ON RWY 24; WERE WE GOING TO CIRCLE? I DIDN'T SEE THE AIRPLANE ON THE RWY; AND I ASKED THE FO IF HE SAW IT AS I TURNED THE HUD INTENSITY DOWN. THE FO REPLIED THAT HE DID THEN SEE THE LIGHT ACFT AND THAT IT WAS CLRING THE RWY. I ALSO SAW THE LIGHT ACFT AS HE TURNED TO EXIT THE RWY AND THE TWR CLRED US TO LAND ON RWY 24. I ACKNOWLEDGED THAT AND THE FO LANDED. I BELIEVE THAT THE MISUNDERSTANDING WAS CAUSED BY A COMBINATION OF FACTORS. THE ATIS WORDING MAY HAVE INTEND TO DESCRIBE AN ILS APCH TO 24; CIRCLING TO LAND 15 R; BUT I UNDERSTOOD IT TO MEAN LANDING RWY 24 AND 15R; AND I'M SURE THAT I DID NOT HEAR THE WORD 'CIRCLING' IN THE RECORDING. BOTH THE FO AND I BELIEVED THAT THE TWR CLRED US TO LAND ON THE RWY ASSOCIATED WITH THE ILS THAT WE HAD INTERCEPTED; AND NEITHER OF US HEARD THE TWR CLR US TO LAND ON 15R; NOR DID WE HEAR THE WORD 'CIRCLE' AT THAT TIME. WE BELIEVED THAT THE TWR WAS INTENDING TO DO US A FAVOR BY OFFERING ANOTHER RWY; BUT WE WERE TOO LOW AND CLOSE TO CONSIDER A CIRCLING MANEUVER. FINALLY; MY HUD DISPLAY WAS APPARENTLY SO BRIGHT THAT IT KEPT ME FROM SEEING THE LIGHT ACFT TAIL ON THE RWY. ALTHOUGH I HAD NO DOUBTS ABOUT THE MEANING OF THE ATIS AT THE TIME; WHEN I THINK BACK ON THE WORDING OF IT; I CAN SEE THAT IT COULD BE INTERPRETED DIFFERENTLY. I RESOLVE TO LISTEN EVEN MORE CLOSELY TO LNDG CLRNCS. (NOTE: WHEN I CALLED THE TWR AFTER LNDG; ON MY OWN; THE TWR CTLR SAID THAT ANOTHER ACFT REPORTED HEARING US CLRED TO LAND ON 15R. NEITHER THE FO NOR I HEARD THAT.) I DO THINK THAT THE WORD 'CIRCLING' SHOULD BE INCLUDED IN THE ATIS; AND IN A LNDG CLRNC; WHEN THAT MANEUVER IS REQUIRED! I WILL ALSO ATTEMPT TO USE THE MINIMUM SETTING NECESSARY FOR CLARITY FOR THE HUD SYMBOLOGY.