A PART 135 PLT EXPERIENCED A NIGHTTIME NMAC WHILE ON FINAL APCH IN CLASS C AIRSPACE. PLT MISTOOK THE TFC CALLED BY TWR TO BE THE SAME TFC CALLED BY TRACON.

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I WAS ON A FLT FROM GRAND RAPIDS; MI; TO FNT; IN A CESSNA 208B. AFTER BEING CLRED TO DSND FROM CRUISE ALT OF 7000 FT BY CLEVELAND CTR I WAS HANDED OFF TO FNT APCH CTL. FNT APCH CLRED ME FOR A VISUAL APCH TO RWY 9; AND SAID 'YOUR TFC IS A LANCE ON R BASE FOR RWY 18.' AT APPROX 10 DME I WAS CLRED TO TWR FREQ AFTER CALLING RWY 18 TFC IN SIGHT. AFTER BEING HANDED OFF TO TWR I WAS 'CLRED TO CONTINUE; TFC ON R BASE.' I AGAIN CALLED THE TFC IN SIGHT; THINKING THAT TWR WAS REFERRING TO THE PREVIOUSLY CALLED TFC BY APCH CTL. AT APPROX 2 MI FINAL I NOTICED A RED BEACON DIRECTLY AHEAD AND SLIGHTLY BELOW ME. AS I CALLED THE TWR ABOUT THE LIGHT AHEAD OF ME; MY LNDG LIGHTS BEGAN TO 'WASH' THE ACFT AHEAD OF ME. I BEGAN A CLBING TURN TO THE R AS THE TWR INSTRUCTED ME TO GAR. AN UNEVENTFUL LNDG FOLLOWED A R 360 DEG TO FINAL. I ASSUMED THAT TWR AND APCH WERE TALKING ABOUT THE SAME ACFT. THEY WERE NOT. APCH CTL DID NOT CALL OUT LCL TFC. USUALLY I EXPECT TO HEAR 'YOUR TFC IS ON BLANK APCH; TWR HAS BLANK NUMBER OF ACFT IN THE PATTERN.' TWR DID NOT SPECIFY THE RWY THAT THE ACFT AHEAD OF ME WAS LNDG ON. I WAS LOOKING FOR R BASE TFC TO RWY 18 AND HE HAD R BASE TFC TO RWY 9. APCH CALLED HIS TFC AS A 'LANCE;' TWR MAY HAVE CALLED HIS TFC AS A 'CESSNA.' I DIDN'T CATCH THE DIFFERENCE.