B737-700 FLT CREW HAS A CLOSE-IN RWY CHANGE ISSUED ON THE SEAVU ONE ARR TO LAX.

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FO WAS FLYING THE SEAVU1 RNAV ARRIVAL TO LAX. APPROACH (SOCAL) CLEARED US TO DESCEND VIA THE SEAVU1 TO RWY 24R. I READ BACK THAT CLEARANCE. FO HEARD THE RADIO COMMUNICATION. WHEN WE SWITCHED TO THE NEXT APPROACH CONTROLLER; HE CLEARED US THE ILS RWY 25R AFTER MUSIK. WHEN HE SAID THAT; I QUERIED HIM ON THE RUNWAY WE WERE CLEARED TO AND HE RESPONDED IT WAS RWY 25R. WE WERE PAST LUVYN ON THE ARRIVAL SO HE GAVE US A VECTOR BACK TO THE COURSE FOR RWY 25R. THE REST OF THE APPROACH AND LANDING WERE NORMAL. NEITHER OF US THOUGHT WE WERE CLEARED TO RWY 25R FROM THE PREVIOUS CONTROLLER AND WE BOTH THOUGHT I HAD READ BACK CLEARED FOR RWY 24R. TRAFFIC WAS LIGHT AND IT WAS VFR. THE FO HAD BRIEFED A PLANNED VISUAL APPROACH TO RWY 24R. WE MAY HAVE BOTH SIMPLY HEARD WHAT WE WANTED TO HEAR FROM THE FIRST APPROACH. WE DEBRIEFED THE EVENT BETWEEN EACH OTHER AFTER LANDING AT LAX. I WILL CHECK IN WITH THE NEW APPROACH CONTROL FROM NOW ON WITH THE INTENDED RUNWAY TO VERIFY IN THE FUTURE INSTEAD OF JUST STATING COMPANY NUMBER AT 12000 FEET DESCENDING VIA THE SEAVU1 (ADD 'FOR RWY 24R').