B737 ON R DOWNWIND REQUEST SHORT APCH TO SMF RWY 16L. TFC ON APCH TO RWY 16R. PIC ACKNOWLEDGED UNVERIFIED CTL CLRNC; APPARENTLY CHANGING LNDG RWYS FOR BOTH ACFT. RESULTANT MISCOORD WITH B737 CAUSES CONFLICT.

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WE WERE ON A R MIDFIELD DOWNWIND AND WERE TOLD TO FOLLOW A 'FOKKER ON A 10 MI FINAL TO RWY 16O.' WE SAW THE FOKKER AND REQUESTED A SHORT APCH TO RWY 16R. AFTER A LONG PAUSE; WE WERE CLRED A VISUAL TO RWY 16(?). I IMMEDIATELY TURNED BASE. AS WE APCHED THE TURN TO FINAL; I ASKED FOR THE FOKKER'S LNDG RWY AND WAS TOLD RWY 16R. I STARTED A R CLBING 360 DEG TURN AND TOLD THE FO TO INFORM TWR. SHORTLY THEREAFTER; TWR INSTRUCTED US TO CLB IMMEDIATELY. THE FOKKER WAS IN SIGHT CONTINUOUSLY UNTIL I EXECUTED THE R CLBING TURN. TCASII GAVE NO ALERT (NOT CLOSE ENOUGH). I HAD EXPECTED THE R BECAUSE WE REQUESTED IT. EVIDENTLY WE WERE CLRED TO THE L. IT WOULD HAVE HELPED IF APCH HAD STATED 'PASS BEHIND/AHEAD OF FOKKER; CLRED VISUAL TO RWY 16L/R.' I WILL REDOUBLE MY EFFORTS TO CONFIRM WITH FO THE LNDG RWY WHEN APCHING PARALLELS. SUPPLEMENTAL INFO FROM ACN 460391: I UNDERSTOOD WE WERE CLRED FOR APCH TO RWY 16L. APCH POINTED OUT TFC THAT I THOUGHT WAS GOING TO RWY 16L ALSO. I THOUGHT APCH WAS CLRING US TO MAKE A SHORT APCH IN FRONT OF THAT TFC.