E145 FLC CHALLENGES ZNY CTLR'S CLRNC. WRONG ACFT CLRNC ISSUED.

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WE WERE ON THE FQM STAR TO EWR. WE WERE CRUISING AT FL330 AND WERE GIVEN CLRNC TO FL310. WE WERE JUST W OF FQM; THIS IS JUST ABOUT THE TIME WE ARE NORMALLY GIVEN A XING RESTR TO CROSS HAYED INTXN AT FL180. AS WE DSNDED FOR FL310; WE WERE GIVEN THE CLRNC TO CROSS HAYED AT FL180 AND MAINTAIN 310 KTS AS WE TRANSITIONED TO IAS. AS WE PASSED THROUGH FL290 THE CTLR ASKED US TO CONFIRM WE WERE AT FL310. WE THOUGHT HE MEANT 310 KTS AND WE SAID NO BUT WE WERE ACCELERATING TO 310 KTS. HE SAID WE WERE NOT GIVEN CLRNC TO DSND AND WE WERE NOW TOLD TO LEVEL AT FL270 AND TURN L OFF OF THE STAR. WE RESPONDED AND COMPLIED AND TOLD HIM THEN THAT WE WERE TOLD TO CROSS HAYED AT FL180. HE SAID WE READ BACK CLRNC FOR OUR COMPANY WHO HAPPENED TO BE JUST IN FRONT OF US. IF THIS IS WHAT HAPPENED; THEN THE CTLR NEVER CORRECTED US ON OUR READBACK. HOWEVER COMPANY SAID THEY WERE STILL AT FL290 AND WERE NOT GIVEN CLRNC TO CROSS HAYED AT FL180. I SPOKE WITH THIS CREW PERSONALLY LATER IN THE DAY AND THEY SAID THAT THE CTLR GAVE OUR FLT; CLRNC TO FL180; AS I THOUGHT. THIS PROB CAME FROM A NUMBER OF FACTORS. BOTH COMPANY ACFT HAVE SIMILAR SOUNDING CALL SIGNS. WE WERE EXPECTING CLRNC TO CROSS THE FIX TO COME AT ANYTIME. WE CHKED ON AFTER COMPANY AND NEVER KNEW THEY WERE ON FREQ. WE WERE ALSO NOT CORRECTED IN A FAULTY READBACK; IF INDEED IT WAS IN ERROR.