A DEPARTING B727 WAS MISTAKENLY ISSUED A HDG AND ALT THAT WAS MEANT FOR ANOTHER ACFT. THE CTLR NOTICED THE WRONG TURN AND ISSUED A CORRECTED HDG; HOWEVER; THE ACFT PENETRATED THE ADJACENT POS AIRSPACE WITHOUT COORD.

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DURING CLBOUT FROM JFK; HDG 220 DEGS; CTLR CLRED US TO 11000 FT. I READ BACK '...CLBING TO ONE; ONE -- ELEVEN THOUSAND.' CTLR THEN CLRED 'ACR X TURN R 090 DEGS.' I READ BACK 'ACR X R TURN 090 DEGS.' THE CAPT REPEATED 'R TURN 090 DEGS' TO ME. DURING THE TURN; ATC ASKED OUR HDG AND I REPLIED 320 DEGS. WE WERE INSTRUCTED TO LEVEL OFF AND TURN L TO 180 DEGS. ATC THEN ASKED WHY WE TURNED AND SAID THAT WE WERE ENTERING ANOTHER CTLR'S AIRSPACE. WE REPLIED WE HAD BEEN CLRED 'R 090 DEGS' AND HAD READ IT BACK. ATC SAID IT HAD BEEN FOR A NAVAJO; NOT US. I NEVER HEARD THE NAVAJO READ BACK NOR THE CTLR TELL US THAT IT WAS FOR ANOTHER ACFT. THE CAPT; THE FE; AND I ALL AGREE THE CLRNC WAS FOR US AND IT WAS 'R TO 090 DEGS.' THIS IS A LONG TURN; BUT DUE TO EWR; LGA AND JFK PROX IT WAS NOT OUT OF THE REALM OF POSSIBILITIES TO AVOID ARR/DEP CORRIDORS. WE HAD NO DOUBT IN THE ACFT AMONG THE 3 CREW MEMBERS WHAT OUR CLRNC WAS AND ATC DID NOT CORRECT THE READBACK; SO I DID NOT RECONFIRM. ATC DID NOTICE US GOING WHERE HE DID NOT WANT US AND CORRECTED THE SIT BEFORE ANY CONFLICTS OCCURRED (TO OUR KNOWLEDGE). SHOULD IT BE PROC TO QUERY ANY TURN GREATER THAN 180 DEGS? THIS WOULD HAVE WORKED HERE; BUT WE ONLY TURNED 100 DEGS BEFORE ENTERING THE NEXT SECTOR. ALSO; IN CONGESTED AIRSPACE/FREQS; THIS IS NOT ALWAYS PRACTICAL NOR SAFE TO QUERY EVERY INSTRUCTION. SUPPLEMENTAL INFO FROM ACN 413490: AFTER DEPARTING JFK RWY 22; DEP CTLR ON 135.9 GAVE US THE FOLLOWING INSTRUCTIONS: 'ACR X; TURN R HDG 090 DEGS; CLB TO 11000 FT.' WE READ BACK THE CLRNC AT APPROX 2000 FT AND TURNED R AND WAS CLBING THROUGH APPROX 3500 FT. WE EMPHASIZED THAT WE HEARD AND READ BACK THE INSTRUCTIONS AS WELL AS TURNED IN EXCESS OF 90 DEGS BEFORE BEING QUESTIONED BY THE CTLR. AFTER DISCUSSING IT WITH THE CREW AND THE CTLR; WE DETERMINED THAT HE HAD GIVEN US THE INSTRUCTIONS INTENDED FOR A NAVAJO UNDER HIS CTL.