ACR MLG DEPARTED AN ARPT OTHER THAN THE ONE ATC CLEARED THE FLT FROM.

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ON THE GND AT ST PETERSBURG-CLEARWATER ARPT (PIE) THE COPLT CALLED WHAT HE THOUGHT WAS PIE CLRNC DELIVERY FOR IFR CLRNC TO RALEIGH-DURHAM (RDU). AFTER 2 ATTEMPTS A VOICE CAME OVER THE RADIO AND TOLD US TO CONTACT TAMPA (TPA) CLRNC DELIVERY ON 133.6. HE CALLED AND ADVISED WE HAD 'INFO XRAY (FROM PIE) AND WERE GIVEN CLRNC TO RDU VIA THE TPA 1 DEP TO MAINTAIN 12000'.' WE THEN TOOK OFF AT PIE AND CALLED TPA DEP 'PASSING 1800' CLBING TO 12000'.' HE SAID; 'ROGER; CLRED TO 12000' AND VERIFY YOUR INITIAL LEVEL OFF ALT WAS 1600'.' I STATED IT WAS '12000' AS PER TPA CLRNC.' WE WERE THEN TURNED OVER TO A CENTER FREQ AND CONTINUED W/O FURTHER INCIDENT. IN REVIEWING THE ABOVE DESCRIBED EVENTS WE HAVE COME TO THE CONCLUSION THAT WE WERE NOT SUPPOSED TO GET CLRNC FROM TPA CLRNC DELIVERY AND THAT TPA THOUGHT WE WERE TAKING OFF FROM TPA. THE TPA 1 DEP WE FLEW IS NOT FOR PIE AND INSTEAD OF CLRNC TO 12000' WE SHOULD HAVE HAD AN INITIAL LEVEL OFF OF 1600' AS IS NORMALLY GIVEN TO DEPS OFF OF PIE. MISTAKES MADE BY THE CREW: 1) NOT INSURING THAT INDEED WE WERE ON THE RIGHT FREQ WHEN WE FIRST CALLED FOR IFR CLRNC. 2) ASSUMING THAT TPA CLRNC DELIVERY HANDLED PIE'S CLRNC (THEY ARE VERY CLOSE TOGETHER AND PIE DOES NOT HAVE A CLRNC DELIVERY FREQ). 3) ASSUMING THAT THE TPA 1 DEP IS ALSO FLOWN OUT OF PIE (THE CHART SHOWS PIE AT THE CENTER NEXT TO TPA). MISTAKES MADE BY ATC: 1) GIVING US THE CLRNC THEY DID! THEY ASSUMED WE WERE DEPARTING FROM TPA AND OVERLOOKED THE ARPT OF INTENDED DPE ON THE CLRNC. CONTRIBUTING FACTORS: 1) BOTH PLTS HAD NEVER BEEN TO PIE BEFORE; THEREFORE WERE NOT AWARE OF THE 1600' LEVEL OFF AND WHICH ALSO HELPED TO LEAD TO THE ASSUMPTION THAT TPA CTLED PIE'S DEP CLRNCS. 2) THE ACFT ARRIVED LATE AND BOTH PLTS WERE IN A RUSH TO GET THE REQUIRED CHKS DONE TO GET THE ACFT OUT ON TIME. CORRECTIVE ACTIONS: PLTS--ALWAYS INSURE THEY ARE TALKING TO THE CORRECT ATC AGENCY DIRECTLY RESPONSIBLE FOR THEIR FLT. ATC--INSURE THEY KNOW WHO THEY ARE TALKING TO BEFORE GIVING CLRNCS. SUPPLEMENTAL INFO FROM ACN 81511: PRIORITY TO TAXI AT ST PETERSBURG INTL I INADVERTENTLY CONTACTED TPA DEP CTL FOR CLRNC TO RDU. HE INSTRUCTED ME TO CONTACT CLRNC DELIVERY ON 133.60.