ACR X RESPONSE WRONG CALL SIGN UNAUTH RWY ENTRY XING. RWY INCURSION.

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THE CAPT AND I WERE OPERATING ACR X OUT OF SEATAC ARPT IN SEATTLE; WA; TO OUR DEST ARPT; PDX; OR. WE WERE INSTRUCTED BY THE GND CTLR TO TAXI TO RWY 34L AND TO HOLD SHORT OF RWY 34R AT TXWY Q. WE WERE TOLD TO MONITOR TWR FOR FURTHER RWY XING INSTRUCTIONS. WE UNDERSTOOD THE TWR TO SAY 'ACR X CROSS RWY 34R AND HOLD SHORT OF RWY 34L. YOU'LL NEED TO HURRY ON ACROSS BECAUSE WE HAVE TFC ON A 2 MI FINAL.' I IMMEDIATELY RESPONDED WITH 'ROGER; EXPEDITE ACROSS RWY 34R TO HOLD SHORT OF RWY 34L;' AFTER WE HAD CROSSED AND WERE IN THE PROCESS OF STOPPING SHORT OF RWY 34L; THE TWR CTLR CALLED US USING A PANICKED TONE OF VOICE TELLING US THAT HE DID NOT CLR US TO CROSS THE RWY; BUT HAD INSTEAD CLRED ACR Y TO CROSS RWY 34R. I IMMEDIATELY RESPONDED THAT WE READ BACK THE CLRNC AS WE THOUGHT WE HAD HEARD IT AND THAT IF IT WAS INCORRECT; HE SHOULD HAVE CORRECTED US AND WE WOULD HAVE CONTINUED TO HOLD OUR POS. SO MUCH TIME ELAPSED THAT WE WERE ABLE TO COMPLETE THE ENTIRE DIALOGUE WITH THE TWR; COME TO A COMPLETE STOP SHORT OF RWY 34L; SET THE BRAKE; THEN LOOK OUT THE WINDOW BEHIND US AND WATCH FOR APPROX 10 SECONDS BEFORE THE AIRPLANE ON A 2 MI FINAL ACTUALLY LANDED ON THE RWY (34R) BEHIND US. ACR Y HAD LANDED ON RWY 34L AND WAS HOLDING SHORT OF RWY 34R WAITING FOR A CLRNC TO CROSS RWY 34R AND TAXI ON TO HIS GATE. IT DOESN'T MAKE SENSE TO US THAT THE CLRNC TO CROSS RWY 34R WOULD HAVE CONTAINED THE STIPULATIVE PHRASE 'AND HOLD SHORT OF RWY 34L;' IF THE CLRNC HAD BEEN INTENDED FOR ACR Y. AT NO TIME WAS THERE A DANGEROUS CONFLICT OF TFC. OUR XING WAS TIMELY AND AT NO TIME EVER IMPERILED ANY OTHER ACFT. IT SOUNDED TO US AS THOUGH THERE WAS TRAINING IN PROGRESS IN THE TWR BECAUSE WE TALKED TO 2 DIFFERENT PEOPLE; 1 MALE -- 1 FEMALE; BEFORE AND AFTER WE CROSSED THE RWY. SUPPLEMENTAL INFO FROM ACN 306218: 'AFTER WE HAD CROSSED; THE TWR OPERATOR; WITH RAISED VOICE STATED; 'ACR YOU TOOK THE CALL FOR ACR Y. ACR X WAS NOT CLRED TO CROSS.' THE FO RESPONDED; 'I READ THE CLRNC BACK AS WE THOUGHT WE HEARD IT; IF IT WAS INCORRECT YOU SHOULD HAVE CORRECTED US.' THE TWR OPERATOR THEN SAID; ALL HE HEARD WAS A 'ROGER.' THE FO DID READ THE CLRNC IN TOTAL AS WE HEARD IT. THERE WAS THEN A CHANGE OF VOICES ON THE TWR AND WE WERE THEN CLRED INTO POS AND CLRED FOR TKOF. WE FEEL WE SHOULD HAVE BEEN ADVISED OF A LIKE CALL SIGN IN THE AREA.