INSTRUCTOR PF A PA28 WITH A PVT PLT TRAINEE TOOK A TKOF CLRNC MEANT FOR ANOTHER PA28 FROM THE SAME FBO; WITH A VERY SIMILAR CALL SIGN. ERROR WAS NOT BROUGHT TO THE RPTR'S ATTN UNTIL HE RETURNED TO THE ARPT AN HR AND A HALF LATER. NO CONFLICT OCCURRED AND PLT ATC REVIEW WAS HELD.

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I WAS WITH MY STUDENT FOR WHICH HE WAS A RATED CURRENT PVT PLT SEEKING HIS INST RATING. HE WAS WORKING THE RADIOS AS DO MOST OF THE STUDENTS; ESPECIALLY IF THEY ARE CURRENT RATED PLTS. WE WERE IN SMA X (XAACC) A PA28-161 WARRIOR CHEROKEE). THERE WAS ALSO ANOTHER SMA Y (XCACC) A PA28-161 WARRIOR FROM THE SAME FLT SCHOOL ON FREQ. MY STUDENT CALLED FOR A CLRNC FOR TKOF WITH A R XWIND DEP. THERE ARE 2 PARALLEL RWYS AT THIS FIELD AND THE FIELD HAS A TRAINING TWR. THE CTLR RESPONDED 'CHEROKEE (ACC) CLRED FOR OPTION CAUTION WAKE TURB FOR LEAR LNDG ON RWY 32R.' (WE WERE ON RWY 32L.) MY STUDENT OR WHICH SOUNDED LIKE MY STUDENT RESPONDED; 'ROGER ACC CLRED' WHICH I WAS AT THE TIME LOOKING AT THE LEAR LNDG TO MAKE A MENTAL NOTE OF THE TFC SHE WAS REFING TO. THIS TOOK PLACE IN A MATTER OF 5 SECONDS OR SO. WITH THIS EVENT MY STUDENT TOOK OFF. I FEEL WHAT MADE IT VERY CONFUSING IS THAT THE CTLR NEVER MADE REF TO ANOTHER CHEROKEE WITH SIMILAR CALL SIGN AND WHICH SHE ALSO RESPONDED WITH ONLY ACC THE LAST 3 NUMBERS OF THE CALL SIGN. THE CTLR NEVER RESPONDED WITH A HOLD SHORT OR ANYTHING OF THAT NATURE. UPON REVIEWING THE TAPE FROM THE TWR; WE NEVER HEARD THE OTHER CHEROKEE'S CALL SIGN OR HIM MAKING CONTACT WITH THE TWR PRIOR TO US CALLING. SO MY STUDENT AND I THOUGHT WE WERE THE ONLY ACFT OR CHEROKEE WITH THE CALL SIGN. THE CONFUSING PART OF THE SIT FOR WHEN WE TOOK OFF OR TAXIED OUT IS THAT THE TWR NEVER LET US KNOW IT WAS THE OTHER ACFT THAT WAS CLRED NOT US. SO WE WERE UNDER THE ASSUMPTION THE WHOLE TIME THAT CHEROKEE ACC WAS CLRED. IT WASN'T UNTIL AN HR AND A HALF AFTER WE HAD RETURNED AND LANDED THAT THE CTLR LET US KNOW WHAT HAD HAPPENED. A COUPLE OF PEERS AND I MET WITH THE TWR CHIEF AND ADDRESSED THE PROB WITH PLTS AND CTLRS ABBREVIATING CALL SIGNS; ESPECIALLY WHEN THEY ARE ON ACFT THAT ARE THE SAME AND ARE FROM THE SAME COMPANY. OUR COMPANY HAS BEEN INFORMED OF THE SIT AND I DO BELIEVE THIS WILL SHED SOME LIGHT ON THE PROB TO CHANGE THE NUMBERS. I WILL MAKE IT A MENTAL NOTE AS TO USE THE FULL CALL SIGN NO MATTER WHAT AND I HOPE CTLRS AND ALL PLTS WOULD ALSO.