FLC TAXIES ONTO RWY WITHOUT TWR CLRNC.

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ATIS STATED RWYS 12 IN USE. IT WAS MY FO'S FIRST MEDIVAC MISSION AFTER COMPLETING HIS CHKRIDE. I MENTIONED TO HIM AS WE BLOCKED OUT THAT RWY 12 WAS IN USE AND THE WINDS WERE FAVORING THOSE RWYS WHEN HE CALLED FOR TAXI. WE WERE TOLD TO TAXI TO RWY 30L; INTXN DEP APPROVED (COMMON PRACTICE FOR OUR OPS). HE RESPONDED 'REQUEST FULL LENGTH' BEFORE I COULD INTERVENE. GND CTL RESPONDED 'ROGER FULL LENGTH APPROVED.' I TOLD MY FO THAT AN INTXN DEP WAS OK FOR MEDIVAC (WE ALWAYS USE FULL LENGTH FOR TRAINING); AND THAT I WANTED TO USE RWY 12R BECAUSE OF THE WINDS. HE CALLED GND AGAIN WITH OUR NEW REQUEST. GND RESPONDED 'ROGER; CLRED TO TAXI ON TO EITHER RWY 12; FULL LENGTH OR INTXN DEP APPROVED.' WE COMPLETED OUR CHKLISTS AS WE NEARED THE RWY; CLRED BOTH DIRECTIONS AND I STATED TO THE FO; 'WE WERE CLRED ONTO THE RWY; RIGHT?' HE SAID YES; SO I CONTINUED ONTO THE RWY INTO TKOF POS. SUDDENLY GND CALLED AND ASKED IF WE HAD ENTERED THE RWY. AS WE RESPONDED 'YES' I REALIZED WE WERE STILL ON GND CTL. I IMMEDIATELY EXITED THE RWY AS QUICKLY AS POSSIBLE; AND SWITCHED TO TWR FREQ. AFTER WE CLRED THE RWY; A SINGLE ENG ACFT PERFORMED A GAR OVER THE INFIELD (WITH NO APPARENT CONFLICT; BUT AS A PRECAUTION ONLY). WE DISCUSSED THE SIT WITH THE CTLRS AND REALIZED THAT THE 4- 5 CALLS BTWN US AND GND CTL CREATED SOME CONFUSION FOR BOTH PARTIES. THE SAME CTLR OFTEN HANDLES BOTH POS AT ODD HRS; BUT I SHOULD HAVE QUERIED THE CLRNC TO TAXI 'ONTO' EITHER RWY 12. CONTRIBUTING FACTORS TO THE MISUNDERSTANDING WERE A VERY INEXPERIENCED FO NOT ACCUSTOMED TO OUR ACTUAL OPS (BUT WHO HAD COMPLETED IOE) AND A VERY FATIGUED CAPT; 1 DAY OFF IN 4 WKS. I ALSO BROKE A STANDARD HABIT PATTERN OF ALWAYS STOPPING MOMENTARILY SHORT OF THE RWY TO CONFIRM CHKLIST COMPLETION AND CALL TWR (IF NO PREVIOUS CONTACT).