SMA GIVEN SEQUENCE FOR TOUCH AND GO AND TRAFFIC TO FOLLOW. HAD WRONG ACFT IN SIGHT AND ENDED UP IN CLOSE PROX TO ACFT HE WAS TO FOLLOW.

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I EXPERIENCED A NEAR MISS ON A CIRCLE TO LAND FROM A LDA APCH INTO 19R AT BUCHANAN. DURING MY ENTRY INTO RIGHT DOWNWIND FOR RWY 32R FROM MY LDA APCH FOR RWY 19R; I HEARD THE CTLR SAY DURING MY EXECUTION OF A CIRCLE TO LAND; 'SMA X CLRED FOR TOUCH AND GO ON 32R; #4. FOLLOW ACFT WIDE RIGHT BASE.' I RESPONDED; 'SMA X LOOKING.' BY THIS TIME I WAS ON MID DOWNWIND. WHEN I WAS ALMOST ABEAM THE TWR ON RIGHT DOWNWIND FOR 32R; I HEARD THE CTLR SAY; 'SMA X; #2; FOLLOW ACFT SHORT FINAL.' I ACKNOWLEDGED; 'SMA X ACFT IN SIGHT.' MY STUDENT AND I HAD IDENTIFIED AN ACFT ON SHORT FINAL FOR RWY 32R. SHORTLY AFTER MY RESPONSE; THE CTLR SAID; 'SMA X; YOU MIGHT WANT TO ANGLE OUT TO THE LEFT.' I THOUGHT THAT HE WAS REFERRING TO THE FACT THAT WE WERE ANGLING IN TOWARDS THE RWY ON THE RIGHT DOWNWIND LEG FOR RWY 32R. IT WAS AT THIS POINT THAT I HAPPENED TO CHK FOR TFC TO MY LEFT AND I SAW TFC 200-300' AWAY AND 50' ABOVE US CONVERGING FROM MY LEFT AND DSNDING FOR A BASE ENTRY. I INSTRUCTED MY STUDENT TO DEVIATE TO THE RIGHT AND WE STARTED A RIGHT 180 DEG TURN FROM DOWNWIND ONTO FINAL AND ADDED POWER TO CLB. CONTRIBUTING FACTORS WERE THE POS RPT OF TFC GIVEN AN THE RADIO PHRASEOLOGY USED. FROM MY PERSPECTIVE; THE ACFT WAS ON A WIDE ENTRY TO RIGHT BASE RATHER THAN ON A WIDE RIGHT BASE LEG. THE CTLR CALLED OUT '#2;' CONFIRMED BY MY STUDENT. I; HOWEVER; HAPPENED TO HEAR ALSO '...FOLLOW ACFT SHORT FINAL;' AFTER THE '#2' PHRASE. I FELT THE CTLR COULD HAVE GIVEN A MORE ACCURATE POS RPT AND ESPECIALLY NOT CALLED OUT '#2' WITH AN ACFT ON SHORT FINAL. RATHER HE SHOULD HAVE CALLED OUT '#3 FOR TOUCH AND GO' WITH A BETTER POS RPT ON TFC. I HAVE NOT RPTED THE INCIDENT AS A NEAR MISS; BUT I SPOKE WITH THE PLT OF THE OTHER ACFT (ALSO AN INSTR AND STUDENT) AND THE INSTR MENTIONED HE HAD US IN SIGHT ALL ALONG. YET HE DIDN'T MANEUVER TO AVOID US UNTIL WE TOOK ACTION AND DIDN'T INQUIRE TO THE TWR ABOUT US AS WE WERE CONVERGING. I CALLED THE TWR OVER THE PHONE AND I SPOKE WITH THE CTLR WHO WAS OPERATING ON THE GND FREQ AT THE TIME OF THE INCIDENT. HE SAID SOME CTLRS WILL NOT COUNT THE TFC ON SHORT FINAL; IN TERMS OF RPTING THE SEQUENCING #. I INTEND TO ASK THE SUPVR OF BUCHANAN TWR TO LISTEN TO THE TAPES TO VERIFY THE RADIO COM. THE FLT WAS MY 1ST OF THE DAY AND MY STUDENT'S ONLY FLT OF THE DAY. I FELT; GIVEN THE SITUATION; I TOOK THE APPROPRIATE EVASIVE ACTION. I ALSO FEEL I WAS NOT AT FAULT GIVEN THE INFO THAT I WAS GIVEN ON MY SECOND COM ABOUT SEQUENCING; BUT I THINK I COULD HAVE GIVEN MORE THOUGHT TO HOW MY SEQUENCING REDUCED SO RELATIVELY QUICKLY FROM #4 TO #2 AND HOW MY TFC WENT FROM A WIDE RIDE BASE TO A SHORT FINAL SO QUICKLY. I ALSO REALIZE NOW THAT IT WAS POSSIBLE THE CTLR WAS REFERRING TO MY FOLLOWING OF THE TFC WHEN HE SAID; 'SMA X; YOU MIGHT WANT TO ANGLE OUT TO THE LEFT FOR TFC ON RIGHT BASE;' THAT WOULD HAVE BEEN A GREAT HELP! THE OTHER ACFT WAS A HIGH FIXED WING TAIL DRAGGER. I AM UNFAMILIAR WITH THE MAKE AND MODEL.