R22 INSTRUCTOR PLT DEPARTS WITHOUT CLRNC AFTER A RWY INCURSION.

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UPON OBTAINING OUR CLRNC FOR A TRAINING FLT; A MISHAP OCCURRED INVOLVING OUR R22 HELI AND THE VGT ARPT GND CTL. UPON STATING OUR INTENTIONS TO GND CTL; THEY INSTRUCTED US TO THE APPROPRIATE RWY; TELLING US TO TAXI TO RWY 30L. THEY WILL NORMALLY TELL US TO HOLD SHORT AND CONTACT TWR. BEING USED TO AND NOT HEARING THOSE INSTRUCTIONS; I REPLIED BACK TO GND; 'DO YOU WANT US TO HOLD SHORT OF RWY 30L?' THE CTLR REPLIED; 'TAXI TO RWY 30L AS INSTRUCTED.' IT DIDN'T SOUND THE SAME; HOWEVER. AFTER TRYING TO RECEIVE CLARIFICATION; WE TAXIED TO RWY 30L NOT HOLDING SHORT. THIS WAS ONE OF THE FIRST CLRNCS OF THIS TYPE THAT THIS PARTICULAR STUDENT AND I HAD DONE. WHILE HE WAS NERVOUS AND I WAS CONCENTRATING ON THE TAXI INSTRUCTIONS; WE DID NOT HOLD SHORT AS WE SHOULD HAVE. WE ALSO HAD THE TWR FREQ IN STANDBY AS A NORMAL PROC. AS WE APCHED RWY 30L; WE DID OUR CLRING TURN LOOKING FOR OTHER TFC AND ALSO CHANGED TO THE TWR FREQ. THE STUDENT; NOT REALIZING I HAD SWITCHED; CHANGED THE FREQ BACK TO GND CTL. AS I RPTED TO WHAT I THOUGHT WAS THE TWR; GND SAID WE WERE NOT CLRED ON THE RWY AND TO EXIT THE RWY AND CONTACT TWR. THINKING WE WERE ON TWR; THIS IS WHERE IT ALL BECAME CONFUSING. AS I RESPONDED TO THE CTLR AND PROCEEDED TO CHANGE THE FREQ; THE STUDENT TOOK THE EXIT RWY INSTRUCTION AS A TKOF CLRNC AND WE WERE ON OUR WAY. I KNOW WE SHOULD HAVE TERMINATED THE TKOF; HOWEVER; WE HAD ALREADY TRAVELED A SHORT DISTANCE DOWN THE RWY. MY REACTION WAS TO CONTINUE; TAKING THE CTLS FROM THE STUDENT. AS WE TURNED XWIND; TWR INSTRUCTED ME TO CALL THEM UPON OUR ARR BACK TO THE ARPT. WHEN I RETURNED AND PHONED THE TWR MGR; HE SAID IT WAS CLR THAT I HAD ASKED FOR CLARIFICATION OF THE DEP INSTRUCTIONS WHICH SHOULD HAVE TRIGGERED ANOTHER RESPONSE. ALTHOUGH I ACCEPT FULL RESPONSIBILITY FOR THIS INCIDENT; I WOULD LIKE TO SUGGEST MORE DIALOGUE WITH GND AND TWR TO PREVENT AN INCIDENT LIKE THIS IN THE FUTURE.