'CLRED AS FILED' AN ACR CREW FLIES 'CLRED AS REQUESTED' FROM SUN; ID.

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AT SUN; CTLR WORKS ALL FREQS; THUS VERY BUSY. WHEN WE WERE SITTING ON THE RAMP PRIOR TO DEP; WE REQUESTED CLRNC TO SEA WITH A VFR CLB DIRECT TO YKM SINCE WX WAS OVER 100 MI VISIBILITY; NO CLOUDS. AT THIS TIME THE CTLR WAS TOO BUSY AND SAID CALL BACK ON THE TAXI OUT TO RWY 13. ON THE TAXI OUT; REQUESTED CLRNC AGAIN. HE SAID EXPECT VFR CLB THROUGH FL180 TO MAINTAIN FL200 DIRECT YKM. THEN HE WAS TALKING TO SOMEONE ELSE ON ANOTHER FREQ. NOW WE WERE HOLDING SHORT OF THE RWY AND HE WAS CLRING A JET FOR TKOF THEN HE SAID TO US 'CLRED TO SEA AS FILED; CLRED FOR TKOF RWY 13.' THE JET WAS JUST LIFTING OFF. I KNEW WE DID NOT HAVE IFR SEPARATION. SO I ASSUMED HE MEANT THE CLRNC WE REQUESTED AND WERE TOLD TO EXPECT. HE ALSO TOLD US TO RPT OUT OF 9000 FT MSL. AT 9000 FT I SAID 'HAILEY TWR; AIRLINE X OUT OF 9000 FT VFR CLB DIRECT TO YKM.' HE SAID ROGER CONTACT ZLC. I SWITCHED OUT OF 10000 FT. I CALLED ZLC AND SAID 'AIRLINE X OUT OF 10000 FT; CLBING VFR THROUGH FL180 TO MAINTAIN FL200.' THEN HE CAME BACK AND SAID ROGER TO AIRLINE X CHKING ON. THEN ABOUT 2 MINS LATER; ZLC CTLR CAME BACK AND ASKED OUR POS. I GAVE IT TO HIM AND SAID 'CLBING DIRECT YKM.' HE THEN TOLD ME THAT IS NOT WHAT WE WERE CLRED TO DO. I DISAGREED AND REALIZED THAT THE SUN CTLR HAD NEVER COORDINATED OUR VFR CLB DUE TO HIS WORKLOAD AND MY MULTIPLE ATTEMPTS TO CONFIRM IT -- WITH THE 9000 FT CALL AND THE CHK-ON WITH SLC. WE WERE STILL VFR AND BELOW FL180 WHEN ALL THIS TOOK PLACE. I FELT THE SUN CTLR HAD CLRED US AS REQUESTED AND HE ALSO BELIEVED THAT HE DID; BUT IN HIS HIGH WORKLOAD HE FAILED TO GET APPROVAL FROM CTR. ALSO; ANOTHER FACTOR WAS I SHOULD NOT HAVE TAKEN THE TKOF CLRNC AT THE SAME TIME AS THE IFR CLRNC.