A STUDENT PLT AND HIS CFI CUT OFF ANOTHER ACFT AS THEY WERE TURNING FINAL FOR RWY 17 AT TIW; WA. AN NMAC OCCURRED WITH OTHER ACFT GOING AROUND.

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ON THE DOWNWIND LEG; THE TWR GAVE A SERIES OF DIRECTIONS TO MULTIPLE ACFT. MY INSTRUCTIONS WERE THAT THERE WAS AN ACFT AT THE SHORELINE ON THE ILS WHO WOULD BE DOING A MISSED APCH AND THAT I WAS TO NOTIFY THE TWR WHEN I HAD THE TFC IN SIGHT. THE TWR THEN WENT ON TO GIVE OTHER DIRECTIONS TO OTHER ACFT. I SAW THE TFC ON FINAL AND INFORMED THE TWR I HAD THE TFC IN SIGHT. THE TWR THEN TOLD ME TO EXTEND MY DOWNWIND AND COME IN BEHIND THE ACFT AND THAT I WAS CLRED TO LAND. I WATCHED THE ACFT PASS MY WINGTIP AND MOVE BEHIND ME. THEN I TURNED TO BASE AND THEN TO FINAL. THE TWR THEN ASKED ME IF I HAD CUT OFF THE OTHER ACFT. SEEING THE OTHER PLANE CLBING OUT IN FRONT OF ME; I INFORMED THE TWR THAT; NO; I HADN'T. THE TWR THEN CONTACTED THE OTHER PLANE AND ASKED HIM IF I HAD CUT HIM OFF; TO WHICH HE SAID ID HAD. THE TWR THEN TOLD ME TO LOOK OFF MY L WINGTIP; AND SLIGHTLY ABOVE ME WAS ANOTHER ACFT. I CONTINUED TO LAND AND THE TWR SAID NOTHING MORE OF THE MATTER. I IDENTED THE WRONG ACFT AND FOLLOWED IT. THE ACFT I WAS TOLD TO FOLLOW WAS FARTHER OUT; ON FINAL. THINGS THAT I COULD HAVE DONE BETTER ARE TO HAVE KNOWN THE EXACT LOCATION OF THE SHORELINE AND THEN IF THERE WAS ANY DOUBT; CONFIRM THAT THE ACFT THAT PASSED MY WINGTIP WAS THE CORRECT ACFT.