AN INST FLT INSTRUCTOR WITH A STUDENT IS BELIEVED TO BE OFF COURSE WHILE COMPLETING A PRACTICE VOR APCH. THE RPTR SUSPECTS THAT THE CTLR TRANSPOSED ARPTS AND THOUGHT THE ACFT WOULD BE FLYING A DIFFERENT HEADING.

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I WAS ON AN INST TRAINING FLT WITH A STUDENT; GOING TO SEVERAL ARPTS TO FLY MULTIPLE APCHS. WE LEFT MGY AND DID A VOR APCH AT ILN; THEN PROCEEDED TO XUB TO DO THE VOR RWY 23 APCH AT RZT TO BE FOLLOWED BY THE NDB RWY 23 APCH AT RZT. AFTER BEING CLRED FOR THE VOR APCH AND FLYING IT; WE RETURNED TO COLUMBUS APCH DURING THE MISSED APCH PROC. THE APCH CTLR QUESTIONED WHY WE WERE SO FAR S AND TOLD US WE WERE DOING THE WRONG MISSED APCH PROC. WE READ THE PUBLISHED MISSED APCH PROC OFF THE APCH PLATE TO HIM; WHICH WE WERE DOING. WE WERE THEN CLRED FOR THE NDB APCH AND PROCEEDED TO GO DIRECT TO THE ROSS COUNTY NDB. WE WERE QUESTIONED AGAIN BY THE COLUMBUS APCH CTLR AS TO WHERE WE WERE GOING. 5 MI TO THE NNE OF RZT IS CYO WHICH ALSO HAS A VOR AND NDB APCH. APPARENTLY THE CTLR THOUGHT WE WERE DOING APCHS AT CYO NOT RZT AND DID NOT EXPECT US TO BE WHERE WE WERE. HE SAID WE REQUESTED THE APCHS AT CYO. WHETHER WE MISSPOKE OR HE MISHEARD US; I REALLY DO NOT KNOW. WHETHER HE CLRED US FOR THE APCHS AT RZT OR SAID WE WERE CLRED FOR THE APCHS AT CYO; I AM NOT POSITIVE; HOWEVER; MY STUDENT AND I BOTH THOUGHT HE SAID RZT. WE THEN CANCELED OUR APCH REQUEST AT RZT AND PROCEEDED WITH THE REST OR OUR TRAINING FLT WITHOUT FURTHER CONFUSION OR PROBS.