ZZZ LCL CTLR DESCRIBED OPDEV WHEN DEP ACFT USED TWO DIFFERENT CALL SIGNS CONFUSING IFR VERSUS VFR STATUS; ACFT DEPARTED WITHOUT RELEASE.

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I WAS WORKING LCL N AND S COMBINED WHEN ACFT X CALLED FOR TKOF. I HAD NO STRIP ON ACFT; VFR OR IFR. I ASKED ACFT TO VERIFY VFR. HE SAID NEGATIVE. I CALLED MYSELF ACR X WITH GND CTL. I DID NOT HEAR HIM SAY NEGATIVE; BUT HEARD HOW HE CALLED HIMSELF ACR X WITH GND CTL. I HAD A VFR STRIP ON AN ACR X AND THOUGHT IF HE CALLED GND CTL AS ACR X THEN HE MUST BE VFR; SINCE THE USE OF ACR X CALL SIGN INDICATES VFR. I ASKED IF HE WAS GOING TO USE THE ACR X CALL SIGN OR THE ACFT X CALL SIGN. HE SAID HE WANTED TO USE THE N-NUMBER CALL SIGN. THIS FLT SCHOOL IS KNOWN TO INTERCHANGE CALL SIGNS DURING FLT SESSION; SO I THOUGHT HE WAS VFR AND WANTED TO CHANGE CALL SIGN IN ZZZ. I CLRED HIM FOR TKOF AND APPROVED HIS DIRECTION OF FLT; NOT KNOWING HE WAS IFR. I DID NOT GET AN IFR RELEASE FOR ACFT. ACFT WENT TO THE IFR APCH FACILITY THEN THE OPDEV WAS DISCOVERED. I BELIEVE THIS OPDEV COULD HAVE BEEN PREVENTED HAD THE FLT SCHOOL FOLLOWED PROCS BY USING IFR CALL SIGN AT ALL TIMES. IF HE HAD USED THE IFR CALL SIGN WITH GND CTL; GND CTL WOULD HAVE KNOWN HE WAS IFR AND WOULD HAVE PASSED THE IFR STRIP TO ME AS THE LCL CTLR. I WOULD HAVE CALLED THE IFR APCH FACILITY FOR ACFT'S IFR RELEASE AND PROPER PROC WOULD HAVE BEEN FOLLOWED ALL THE WAY THROUGH. THOUGH I DIDN'T HEAR ACFT ANSWER MY QUESTION; PLT COULD HAVE HELPED BY SAYING IFR OR NOT. MY FOCUS WAS SHIFTED BY LISTENING TO HIM EXPLAIN TO ME HIS COM WITH GND CTL.