A PA28 WITH INSTRUCTOR AND TRAINEE ON VFR PRACTICE APCH IS ASSIGNED A CLB FROM 2500 FT TO 3000 FT BY A BUSY APCH CTLR. SHORTLY THEREAFTER A MIL LR35 WAS ISSUED A DSCNT TO 3000 FT AND CAME IN CLOSE PROX TO THE PA28. THE RPTR BELIEVES THAT THAT CTLR ISSUED THE CLB TO 3000 FT TO THE WRONG ACFT.

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NMAC OCCURRED DURING AN OTHERWISE ROUTINE INST TRAINING FLT. AFTER COMPLETING A VFR PRACTICE APCH AT 1A9 WE TURNED E AND CALLED MXF APCH TO REQUEST A PRACTICE LOC APCH AT MXF. WE WERE GIVEN A VECTOR OF 070 DEGS AT 2500 FT. AT THIS TIME I HEARD AT LEAST 3 OTHER ACFT BEING VECTORED TO THE SAME APCH. APCH TOLD US TO CLB AND MAINTAIN 3000 FT. STUDENT REPLIED; 'OUT OF 2500 FT FOR 3000 FT.' CTLR SAID; 'ROGER.' APCH THEN TOLD THE LEAR TO DSND TO 3000 FT. THE LEAR WAS NBOUND BEING VECTORED FOR THE APCH. CTLR TOLD US TFC WAS PASSING W TO E AT 3 MI. WE HAD STARTED OUR CLB AND WERE AT 2800 FT. I JUST CAUGHT SIGHT OF THE LEAR WHEN APCH SAID 'NGA X; I SEE YOU'RE CLBING; TFC AT 1 1/2 MI.' THE LEAR WAS HEADED RIGHT AT US IN A L TURN. I TOOK CTL FROM THE STUDENT AND TURNED US AWAY FROM THE LEAR. THE CTLR THEN TRIED TO TELL US THAT WE WERE AT THE WRONG ALT. WE REMINDED HIM OF OUR EARLIER DIRECTION TO CLB TO 3000 FT. AFTER IT WAS SORTED OUT; WE COMPLETED THE FLT WITH NO FURTHER COMPLICATIONS. I DON'T KNOW IF THE LEAR SAW US. I'M NOT ONE TO POINT FINGERS; BUT I BELIEVE THE CTLR TOLD THE WRONG ACFT TO GO TO 3000 FT. CONTRIBUTING TO THE SIT WERE THE OTHER ACFT BEING VECTORED TO THE APCH; THE CTLR WORKING ACFT TO ANOTHER ARPT (MGM); THE CTLR'S USE OF NONSTANDARD TERMINOLOGY IN DESCRIBING THE TFC TO US; AND THE FACT THAT WE WERE IN A TRAINING FLT AND WERE DOING A LOT OF TALKING WITH THE STUDENT. I SHOULD HAVE PICKED UP ON THE CO-ALT ASSIGNMENT; BUT THE LACK OF TFC ADVISORY LED ME TO BELIEVE THE TFC WAS FAR AWAY.