MD80 CREW INCORRECTLY HEAR TFC CALL FROM TWR; SMF.

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I WAS OPERATING AN SD3 ACFT. MY RTE OF FLT WAS RNO VIA V-392 TO SMF AT 12000 FT MSL. AFTER RECEIVING SEVERAL RADAR VECTORS FROM SIERRA APCH CTL; INCLUDING ALT DSCNTS AND HDG CHANGES. I WAS EVENTUALLY VECTORED TO A L DOWNWIND AT 3000 FT MSL FOR A VISUAL APCH TO RWY 34L AT SMF. APCH CTL ALERTED ME TO THE POS OF A DC10 AHEAD AND LOWER THAT WAS ALSO CLRED FOR A VISUAL TO RWY 34L. UPON BEING CLRED FOR A VISUAL APCH TO RWY 34L AND A CHANGE TO TWR FREQ (125.70); I NOTIFIED TWR THAT I WAS ABEAM THEIR POS AND WAS GOING TO STAY SLIGHTLY HIGHER AND 5 MI BEHIND THE DC10 FOR TURB SEPARATION. TWR CALLED MY 5 MI SEPARATION AND CLRNC TO LAND; AND I BEGAN A L BASE TURN TO FINAL. USING THE ILS AS A BACKUP LNDG AID; I ESTABLISHED MYSELF ON FINAL APCH AND SLIGHTLY ABOVE (1/2 DOT) GS. APPROX 3 MI FROM RWY THRESHOLD; I NOTICED A SERIES OF BRIGHT LIGHTS AT MY QUARTERING L FRONT AND LOWER POS. WITHIN SECONDS; I REALIZED THAT THIS WAS ANOTHER ACFT THAT HAD CUT IN FRONT OF ME AND THAT THE ACFT WAS LARGE. AT ABOUT THE SAME TIME; TWR CALLED 'MD80; YOU JUST CUT IN FRONT OF A SHORTS ON FINAL.' 'SD3; TAKE WHATEVER ACTION IS NECESSARY.' IN A BRIEF MOMENT; BOTH THE MD80 AND I BROKE INTO A L CLBING TURN. UPON SEEING HIS TURN; I RE-ENTERED FINAL AND COMPLETED A NORMAL LNDG. AFTER SECURING MY ACFT; I CALLED TWR BY TELEPHONE AND ASKED -- IN THEIR OPINION -- WHAT HAD HAPPENED? THE GENTLEMAN ON THE OTHER END EXPLAINED THAT 'AN MD80' HAD BEEN CLRED FOR A VISUAL APCH TO RWY 34L; BEHIND THE 'SHORTS' ON FINAL. HE FURTHER EXPLAINED THAT THE MD80 PLT THOUGHT HE HEARD 'ACR Z; YOU'RE CLRED FOR A VISUAL APCH TO RWY 34L BEHIND THE ACFT ON SHORT FINAL.' A NEAR MISS THAT COULD HAVE BEEN CATASTROPHIC.