2 B737-300 FLTS WITH SIMILAR SOUNDING CALL SIGNS ENTER AN AREA OF CONFUSION WITH SCT TRACON WITH ACFT MAKING A WRONG RWY APCH TO LAX; CA.

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I WAS THE CAPT ON A COMMERCIAL FLT FROM OAK TO LAX. OUR NUMBER CALL SIGN WAS CHFG. RIGHT BEHIND US WAS ANOTHER COMPANY ACFT WITH A NUMBER CALL SIGN OF CAFG DSNDING OVER POINT SADDE. WE WERE TOLD TO EXPECT RWY 24R. OVER SMO; WE HEARD WHAT WE THOUGHT THE CTLR SAY 'COMPANY CAFG EXPECT RWY 25L.' CAFG ACKNOWLEDGED THE RADIO CALL. THIS CALL MAY HAVE BEEN TO US; CHFG. WE STILL ANTICIPATED RWY 24R. LATER; IT WAS EVIDENT THAT THE CTLR WAS TRYING TO SEQUENCE OUR ACFT TO RWY 25L; BUT CALL SIGN ASSIGNMENT AND ACKNOWLEDGEMENT WERE BECOMING CONFUSING. WE WERE TOLD TO FOLLOW WHAT WE THOUGHT WAS AN ACFT TO RWY 24R. APCH CTL MAY HAVE MADE A CALL TO US TO FOLLOW AN ACFT TO RWY 25L; BUT COMPANY CAFG ACKNOWLEDGED THE CALL (BLOCKED RADIO CALL). WE TURNED A R BASED TO FINAL ON RWY 24R AND APCH ASKED US TO CONFIRM OUR RWY. WE STATED RWY 24R. WE WERE ISSUED MISSED APCH INSTRUCTION AND COMPLETED A R-HAND PATTERN FOR A NORMAL LNDG ON RWY 24R. IN SPEAKING WITH ATC; IT WAS EVIDENT THAT THE SIMILAR CALL SIGNS CAUSED MUCH CONFUSION. I SPOKE WITH THE CAPT OF FLT CAFG AND SHE STATED SHE WAS HAVING A HARD TIME UNDERSTANDING THE CTLR'S CALL SIGN DIRECTIONS. ALSO; SEVERAL CALLS MAY HAVE BEEN BLOCKED OR MISACKNOWLEDGED. BIG PROB -- THE CALL SIGNS WERE TOO SIMILAR. ALSO; DUE TO THE BUSY SIT; CONFIRMATION OF CALL SIGNS AND DIRECTIONS; BY ALL PARTIES; COULD HAVE BEEN MORE DILIGENT. SUPPLEMENTAL INFO FROM ACN 458649: CTLRS AND CREWS WERE ALL AWARE OF THE SIMILAR SOUNDING CALL SIGNS. IN ADDITION; APCH WAS VERY BUSY WITH MANY OTHER ACFT APCHING LAX. CALL SIGNS AND DIRECTIONS WERE CONFUSED NUMEROUS TIMES; OFTEN BOTH ACFT ANSWERING EACH OTHER'S DIRECTIONS. THE COMPANY HAS BEEN MADE AWARE OF THE HAZARDS OF SIMILAR SOUNDING CALL SIGNS. OTHER THINGS THAT WOULD HELP ARE THE REDUCING OF SATURATION OF RADIO FREQS AT BUSY ARPTS AND GREATER SEPARATION OF APCHING ACFT.