AN A320 CREW; DSNDING INTO LAX; RESPONDED TO A CLRNC ATC PROFESSES WAS FOR ANOTHER ACFT.

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WE WERE ON THE PARADISE FOUR ARR TO RWY 25L AT 270 KTS. SHORTLY AFTER PASSING KONZL; ATC ISSUED THE FOLLOWING CLRNC: 'ACR XYZ CHANGE RWY TO RWY 24R VIA THE MITTS ARR; GO DIRECT TO SNRKL.' I READ BACK THE CLRNC AS STATED. I ACTIVATED THE SECONDARY FLT PLAN WHICH WAS LOADED WITH RWY 24R/PARADISE 4 ARR. I ASKED FO IF HE HAD FOUND SNRKL AND HE SAID YES AND IMMEDIATELY PUT SNRKL IN HIS FMGC. WE WERE GOING DIRECT TO SNRKL AND DSNDING TO 12000 FT. I WAS CHANGING TO THE RWY 24R TRANSITION. ATC ISSUED THE FOLLOWING: 'ACR XYZ CLRED ILS RWY 25L VIA PARADISE FOUR ARR.' I READ BACK THE CLRNC AND ASKED APCH TO CONFIRM THE RWY BECAUSE WE HAD JUST BEEN CLRED FOR RWY 24R VIA MITTS ARR. APCH SAID THAT WAS FOR A COMPANY ACFT; ACR XYZ WAS CLRED FOR THE APCH TO RWY 25L VIA PARADISE FOUR ARR. WE TURNED L TO RE-INTERCEPT THE PARADISE FOUR ARR BTWN RIFFT AND PDZ. WE HAD BEEN DSNDING TO 12000 FT. AS WE TURNED BACK TO INTERCEPT THE PARADISE FOUR ARR; WE WERE E OF RIFFT INTXN AT 13500 FT. ATC ADVISED US WE SHOULD BE AT 14000 FT. I ACKNOWLEDGED WE WERE CORRECTING THE ALT. AT PDZ ATC CLRED US DIRECT ARNES MAINTAIN 10000 FT AND CLRED APCH RWY 25L AFTER SUZZI. THE APCH WAS AS NORMAL AS CAN BE EXPECTED FOR LAX AFTER ARNES. THERE WAS AN ACR XYA ON THE FREQ WHO USED RWY 24R; BUT I DON'T KNOW WHAT HIS CLRNCS WERE. THE FO CALLED SOCAL APCH AFTER WE LANDED. THAT INDIVIDUAL ACKNOWLEDGED THERE WAS SOME MISCOM WITH US. HIS STATEMENT OF MISCOM WAS; INCORRECT CLRNC ISSUE; READBACK; OR WRONG ACFT READBACK. HE ALSO SAID THERE WAS NO CONFLICT CREATED; SAW NO PROB AND SAW NO REASON FOR ANY PAPERWORK BEING FILED. THE FO AND I ARE 99% SURE WE RECEIVED A CLRNC TO RWY 24R AND THAT I READ BACK THE CLRNC TO RWY 24R WITH NO CORRECTION FROM ATC.