ACR WDB TOOK CLRNC MEANT FOR ANOTHER WDB AND STARTED PREMATURE TURN AND DESCENT.

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WE WERE 10 MI W OF JFK BEING VECTORED FOR AN APCH TO THAT ARPT. OUR CALL SIGN WAS ACR EJ (WDB X) AND WE WERE AT AN ALT OF 15000' AND A HDG OF 180 DEGS. I WAS FLYING AT THE TIME. THE F/O; IN RESPONSE TO A RADIO CALL WHICH I DID NOT HEAR; SAID; 'ROGER ACR 'EJ' (WDB X) LEFT TO 020 AND DES TO 2000'.' I DID NOT HEAR THE CTLR ACKNOWLEDGE. I BEGAN SHALLOW BANK AND A GRADUAL DES WHILE I ASKED THE F/O TO RECONFIRM THE INSTRUCTIONS. THE FREQ WAS VERY BUSY AND HE HAD TROUBLE GETTING APCH CTL TO ANSWER. I STOPPED MY DES AT 14500' AND JUST AT THAT TIME APCH CTL CALLED US SAYING; 'ACR 'EJ' WDB X; WHERE ARE YOU GOING?' AS THE F/O ANSWERED THE RADIO I IMMEDIATELY RETURNED THE ACFT TO ITS ORIGINAL HDG AND ALT. IT WAS DETERMINED THAT WE HAD TAKEN A HDG AND ALT CHANGE MEANT FOR ACR 'JN' WDB Y. I HIGHLY RECOMMEND 2 THINGS: 1) THAT WE RETURN TO AN EARLIER POLICY OF READING BACK NUMBERS ONE DIGIT AT A TIME. FOR EXAMPLE; SAYING 'ONE SIX' RATHER THAN '16;' AND 'SIX ZERO' RATHER THAN '60.' 2) THAT CTLRS WAIT FOR ACKNOWLEDGEMENT BEFORE PROCEEDING TO THE NEXT ITEM OF BUSINESS. THAT IS DIFFICULT WHEN THINGS ARE BUSY; BUT THAT IS WHEN IT IS NEEDED MOST. FOR MY PART; IF I'M NOT ABSOLUTELY CERTAIN THAT AN INSTRUCTION IS FOR MY FLT; I'LL CONFIRM BEFORE ACTING ON IT. NO CONFLICT IN AIRSPACE RESULTED FROM THE ABOVE. SUPPLEMENTAL INFORMATION FROM ACN 80270: THERE WAS ACR B 'JN' WDB Y ON THE FREQ. WITH THE CTLR'S RADIO DIFFICULT TO UNDERSTAND; THE DIFFERENCE BTWN 'JN' AND 'EJ' WOULD BE DIFFICULT TO HEAR. THE CTLR WAS WORKING 3-4 ACR A FLTS. ALONG WITH THE ACR B AND POSSIBLY OTHERS. HE MAY HAVE SAID ACR A 'EJ' WDB X/ACR B 'JN' WDB Y OR ANY COMBINATION OF THE TWO. I WAS PREOCCUPIED WITH TUNING THE ILS FREQ AND IDENTIFYING.