B737-300 FLT CREW PERFORMS A GAR AFTER SEEING ANOTHER ACFT XING THEIR ASSIGNED RWY 10R AT BOI; ID.

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WITH FO FLYING; WE ESTABLISHED A DOWNWIND TO BOI RWY 10R. ABEAM THE ARPT; I INQUIRED WITH APCH IF OTHER ACFT WERE DOING VISUALS OR STAYING ILS. I COULD SEE ARPT FROM OUR CURRENT POS AND THOUGHT WE COULD EXECUTE A VISUAL FROM THAT POINT. APCH RESPONDED 'YES' AND ASKED IF WE HAD ARPT IN SIGHT.' I SAID 'YES.' HE CLRED US FOR 'VISUAL TO RWY 10R.' THE FO TURNED INBOUND AND WASN'T SURE IF SHE HAD ARPT IN SIGHT. I GAVE INITIAL HDGS TO IT AS I DID SEE THE ARPT. I THEN CALLED THE TWR AND THEY CLRED US TO LAND RWY 10L. RIGHT AFTER THAT; THE FO SAID SHE DID NOT SEE ARPT; AND ASKED ME TO TAKE ACFT; WHICH I DID. I FLEW IT TO RWY 10R AND; AT ABOUT 300 FT; NOTICED ANOTHER ACFT TAKE THE RWY. I EXECUTED A GAR. WE INQUIRED WHY ACFT WAS ON RWY 10R AND TWR REPLIED WE WERE CLRED FOR LNDG RWY 10L. WE FINISHED THE GAR AND CAME BACK TO LAND ON RWY 10R USING THE ILS UNDER VISUAL CONDITIONS. I BELIEVE FACTORS WERE CONFUSING CLRNCS AT SAME TIME OF CHANGING CTL OF ACFT COMBINED WITH SOME LEVEL OF PLT FATIGUE AS THIS WAS OUR 4TH LEG OF A LONG DAY. THE LNDG CLRNC CAME RIGHT AS I WAS CONCERNED THAT FO COULD SEE RWY. I ACCEPTED IT AND IMMEDIATELY BECAME PF. FO DID NOT HEAR THE LNDG CLRNC AS SHE WAS TRYING TO SEE ARPT. SUPPLEMENTAL INFO FROM ACN 605313: I FELT THE CONFUSION WAS CAUSED PARTLY BY THE CLRNC FROM AN ILS TO A VISUAL AND NO CLR VERBIAGE ABOUT A RWY CHANGE (IE; NOW CLRED).