CPR LTT TOOK OFF WITHOUT RECEIVING AIRWAYS CLRNC.

Narrative

WE LANDED AT JAX TO DROP OFF A PAX AND REPOS TO ST AUGUSTINE; FL. ORIGINALLY WE HAD PLANNED TO GO TO MIAMI AND A FLT PLAN IFR HAD BEEN FILED. AS THE COPLT WAS LETTING OUR PAX OFF; I CALLED AND CLRNC GAVE ME A CLRNC TO MIAMI. I TOLD THE CTLR THAT OUR PLANS HAD CHANGED AND REQUESTED 'A TWR TO TWR CLRNC TO ST AUGUSTINE.' THE CTLR ASKED WHAT ALT I WANTED AND I REPLIED 3000 FT. ABOUT THIS TIME THE COPLT RETURNED TO HIS SEAT AND TOOK OVER COMS AGAIN. THE CTLR CAME BACK AND GAVE US A DEP FREQ AND SQUAWK. WE TAXIED OUT AND TOOK OFF UNDERSTANDING WE HAD AN IFR CLRNC. WE CONTACTED DEP CTLR AS WE WERE ENTERING THE BASE OF THE CLOUDS AT 2300 FT. THE CTLR ASKED IF WE WERE IFR AND WE RESPONDED THAT WE UNDERSTOOD WE WERE. THE CTLR REPLIED THAT HE DID NOT SHOW US AS IFR; BUT QUICKLY GAVE US A CLRNC TO SGJ. A FEW THINGS HAPPENED HERE THAT NEED MORE THOUGHT. 1) I SHOULD HAVE BEEN MORE SPECIFIC AND SAID IFR. 2) THE CTLR SHOULD HAVE QUESTIONED A REQUEST FOR A VFR CLRNC OUT OF THE TRSA AT 3000 FT WHEN THE CEILING WAS RPTED AS 2000 FT (IF THEY UNDERSTOOD IT TO BE A VFR REQUEST). 3) THE CHANGING OF ROLES OF THE PLT AND COPLT IN THE COM TO ATC. ONE OR THE OTHER SHOULD HANDLE THE WHOLE ACTION PERHAPS.