SIMILAR SOUNDING A/N AND RESPONSE TO WRONG CALL SIGN CREATES CONFUSION FOR FLCS AND ATC APCH CTLR.

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WE WERE OPERATING ABOUT 1 HR LATE WHICH PUT US IN NY AREA AT SAME TIME AS FLT ADB. OUR FLT WAS ABB. CTLR CLRED ABB DIRECT LGA DSND AND MAINT 4000 FT. WE WERE AT 9000 FT. I ACKNOWLEDGED AND WE COMPLIED. WE HAD NOT HEARD ADB ON FREQ YET; NOR HAD WE HEARD HIM RESPOND TO SAME CLRNC. WE HAD BLOCKED EACH OTHER AND NOT KNOWN IT UNTIL PHONE CONVERSATION LATER. SUDDENLY; CTLR SAID; 'ADB WHERE ARE; YOU GOING?' ADB; 'YOU CLRED US DIRECT DOWN TO 4000 FT. ATC WAS SILENT FOR ABOUT 10 SECONDS. SEEMED LONGER. ATC SAID ABB TURN R HDG 150 DEGS. A TARGET SHOWED ON TCASII AT 12 O'CLOCK; 2000 BELOW US. IF WE HAD CONTINUED DOWN; WE WOULD HAVE HAD A NEAR MISS. ATC CONTINUED TO GIVE BOTH ABB AND ADB A LOT OF STRANGE VECTORS -- OBVIOUSLY FOR TFC. I QUERIED ATC ABOUT IT AND HE SAID 'YOU GUYS KEEP GETTING YOUR FLT NUMBERS MIXED UP.' I KNOW HE HAD SAID ABB IN THE ORIGINAL CLRNC; BUT HE MEANT IT FOR ADB. ALSO; ADB WAS EXPECTING THAT CLRNC SO HE RESPONDED. IN RETROSPECT; IT WAS STRANGE THAT WE WOULD BE CLRED FROM 9000 TO 4000 FT IN SUCH A HIGH DENSITY AREA. I THOUGHT MAYBE THE TFC WAS LIGHT AT THAT TIME. SUPPLEMENTAL INFO FROM ACN 266985: PRETTY SOON; WE HEARD APCH ASKING; '(COMPANY) ADB WHAT'S YOUR HDG AND ALT?' WE WERE UNAWARE THAT THERE WAS AN ADB ON THE FREQ BUT THEY RESPONDED THAT THEY WERE PROCEEDING DIRECT LGA AND DSNDING TO 4000 FT. THE CTLR GAVE THEM A TURN TO THE S; WHICH THEY RESPONDED TO WHILE PROTESTING THAT THEY HAD BEEN CLRED DIRECT LGA. THE CTLR AGAIN GAVE ADB A TURN TO THE S. WE THEN TOLD HIM THAT ABB WAS PROCEEDING DIRECT LGA AND DSNDING TO 4000 FT. HE THEN GAVE US A TURN TO THE S AND TOLD US TO STOP THE DSCNT AT 9000 FT. SUPPLEMENTAL INFO FROM ACN 266990: WE WERE FLT ADB; SIMILAR SOUNDING CALL SIGN (WITH FLT ABB); TOOK OUR CLRNC TO DSND AND PROCEED DIRECT TO LGA. CTLR ALSO WAS CONFUSED AS TO WHICH ACFT WAS WHICH. I CALLED ATC ON LAND LINE JUST TO CONFIRM ALL WAS OK. HE CONFIRMED NO PROBS.