MULTIPLE RWY OP PARALLEL RWYS CTLR CLRED SMA X TO LAND ON WRONG RWY CREATING NMAC WITH CPR JET ON PARALLEL RWY. OPDEV.

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I HAD BEEN PRACTICING FULL STOP TAXI BACK TKOF AND LNDGS ON RWY 9L. ON THE LAST LNDG I WAS LINED UP ON RWY 9L (FINAL) AND EXPECTING A LNDG CLRNC TO RWY 9L. FCM TWR GAVE ME A CLRNC TO LAND ON RWY 9R WHICH IS THE LIGHTED RWY. IT WAS NEARING OFFICIAL SUNSET. I CLRED MY TURN AS WELL AS POSSIBLE AND PROCEEDED TO STEP OVER TO RWY 9R. FCM TWR CLRED ANOTHER PLANE TO LAND ON RWY 9R AND THAT IS WHEN I WAS TRYING TO VERIFY WITH TWR IF I WAS CLRED TO LAND RWY 9R AS INSTRUCTED. THERE WERE MANY ACFT AND CHATTER ON THE FREQ. IMMEDIATELY AFTER THE OTHER ACFT WAS GIVEN THE CLRNC I STARTED A GENTLE TURN BACK TO RWY 9L AND THAT'S WHEN THE PLT OF A CORPORATE JET APPEARED ON SHORT FINAL FOR RWY 9R. AT THAT TIME HE WAS IN FRONT OF ME AND TURNING TO THE R. I SAID I WAS GOING TO THE L AND TURNED SHARPLY. AFTER A REVIEW OF THE TWR TAPES THE CTLR CONFIRMED THAT HE HAD GIVEN ME CLRNC TO LAND RWY 9R WHEN HE MEANT RWY 9L. MAIN CONTRIBUTING FACTOR WAS A WRONG CLRNC AND NOT RECEIVING A READ BACK FROM MYSELF. A CONTRIBUTING FACTOR WAS A CONGESTED FREQ AND CTLR WORKLOAD AT THAT PARTICULAR TIME. BOTH MYSELF AND THE CORPORATE PLT; I BELIEVE; TOOK CORRECT AND PROMPT EVASIVE ACTION.