A B737-300 CREW READ BACK A DSCNT CLRNC MEANT FOR COMPANY ACFT FOLLOWING BEHIND. THE CAPT READ BACK THE PROPER CALL SIGN AND CLRNC WITH NO CORRECTION FROM ATC.

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WE WERE FLYING FLT ABC; A B737-400. FLT ABD (ANOTHER B737-400) GOING TO PSP WAS RIGHT BEHIND US AND ON THE SAME FREQ. WE WERE NEAR THE TOP OF DSCNT POINT AND ANTICIPATING A DSCNT CLRNC. I WAS FLYING; THE FO WAS ON COMPANY RADIO GETTING A GATE ASSIGNMENT AND ATIS WHEN ZLA GAVE US A DSND NOW TO FL280 FOR TFC AND THEN TO FL240 PLT'S DISCRETION. I READ THE CLRNC BACK; 'THIS IS FLT ABC DSND NOW TO FL280 AND THEN PLT'S DISCRETION TO FL240.' HE SAID THAT'S CORRECT. FLT ABD WAS ON THE SAME FREQ. I STARTED TO DSND AND THEN NOTICED A POSSIBLE TFC CONFLICT ON THE MAP. I STOPPED THE DSCNT AT ABOUT FL318 AND STARTED A SLOW CLB. THE FO HAD COME BACK ON RADIO #1 (ATC) AND I EXPLAINED THE CLRNC TO HIM. WE GOT A TA AND I CONTINUED TO CLB AND GOT AN RA WHICH SAID 'DON'T DSND.' ATC ASKED FOR OUR ALT AND THE FO RESPONDED. ZLA SAID CLB BACK TO FL330. HE RESPONDED AND MENTIONED THAT WE HAD BEEN CLRED LOWER. THE ATC CTLR SAID THE CLRNC WAS FOR FLT ABD. FLT ABD DIDN'T RESPOND TO THE CLRNC AND MUST HAVE ALSO THOUGHT IT WAS FOR US OR MISSED IT. WE SPOKE TO THE ZLA SUPVR WHO HAD PULLED THE TAPE. HE SAID THAT I DID READ BACK THE CLRNC AS FLT ABC AND GOT AN 'OK' FROM THE CTLR; BUT THAT THE CTLR HAD CALLED IT FOR FLT ABD. THE SUPVR SAID THAT IT WAS AN OPERROR. WE HAVE ASKED OUR COMPANY NOT TO RUN SIMILAR FLT NUMBERS TOGETHER; BUT IT STILL HAPPENS. HOPEFULLY; THIS PROC CAN BE CHANGED. SUPPLEMENTAL INFO FROM ACN 459366: IT WAS JAN/XA/00; AND AIRSPACE OVER SOUTHERN CALIFORNIA WAS SATURATED WITH AIRPLANES.