ACR WDB DEVIATED FROM CLRNC ROUTE. FLEW THE WRONG SID OUT OF ANC.

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F/O OBTAINED IFR CLRNC FROM ANC CLRNC DELIVERY. THERE WAS SLIGHT RADIO INTERFERENCE AT BEGINNING OF CLRNC HOWEVER F/O AND I BOTH WERE LISTENING TO CLRNC AND UNDERSTOOD THAT WE WERE CLRD BY THE ANC SID. THE CLRNC WAS READ BACK TO CLRNC DELIVERY AND CONFIRMED BY CLRNC DELIVERY. THE SID WAS INSERTED INTO THE CDU AND THE RESTRICTION RADIALS WERE ALSO ENTERED. AFTER TKOF THE CLRNC CALLS FOR TURNING RIGHT TO 190 DEG AT 2000' MSL AND XING THE ANC 105 DEG RADIAL BELOW 5000 MSL. F/O ASKED DEP CTL IF WE COULD CONTINUE CLIMB TO 14000 AND ELIMINATE THE 5000 XING RESTRICTION. DEP CTL ADVISED WE WERE SUPPOSED TO HAVE TURNED LEFT ON A KNIK SID INSTEAD OF AN ANC SID. DEP CTL ADVISED TO CONTINUE CLIMB AND TURN RIGHT TO 330 DEG AND CLRD DIRECT TO GKN BY RNAV. WE ADVISED WE HAD COPIED AND READ BACK AN ANC SID. THE WX WAS 60 SCATTERED 100 SCATTERED 60 MI SO WX WAS NO PROBLEM AND THERE WERE NO OTHER ACFT IN THE VICINITY OF THE ARPT REGION SO NO SAFETY PROBLEMS WERE ENCOUNTERED. THE F/O AND I BOTH UNDERSTOOD WE WERE CLRD BY AN ANC SID AND WROTE THAT DOWN AND READ THAT CLRNC BACK TO CLRNC DELIVERY. CLRNC DELIVERY CONFIRMED THAT READBACK. POSSIBLY CLRNC DELIVERY GAVE US ANOTHER SID AND WE COPIED WHAT WE WERE EXPECTING TO HEAR. AT THE SAME TIME WHEN WE READ BACK THE CLRNC; THEN CLRNC DELIVERY COPIED WHAT HE WAS EXPECTING TO HEAR. THE OLD ADAGE OF 'CONTINUED VIGILANCE' BY EVERYONE INVOLVED IS STILL VALID.