ACR X UNAUTH TKOF ON OCCUPIED RWY HAD LTSS FROM ACR Y AND ABORTED TKOF.

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ACR X RECEIVED TKOF CLRNC FROM RWY 16L AT SEATTLE (APPARENTLY CLRNC WAS FOR ANOTHER ACFT); READ BACK CLRNC ALONG WITH APPROPRIATE CALL SIGN. AS WE WERE SETTING TKOF PWR AND COMPLETING TKOF CHKLIST. NOTICED ACR Y STILL ON RWY DOWNFIELD (SAME RWY) SLOWED DOWN AND TAXIED OFF RWY BECAUSE IT WAS APPARENT THAT BOTH ACFT WERE GOING TO DEPART TOO CLOSE TO EACH OTHER. ADVISED TWR AND WERE TOLD THAT WE WERE NOT CLRED FOR TKOF. WE THEN TAXIED BACK TO TKOF. I BELIEVE THIS WAS SIMPLY AN ERROR IN COM AND MY ONLY SUGGESTION FOR PREVENTION OF A RECURRENCE WOULD BE CLARIFYING VERBIAGE ON RADIO AND CTLR LISTENING TO MAKE SURE PROPER ACFT ANSWERS INSTRUCTIONS. WE ALSO SHOULD HAVE BEEN LISTENING FOR ACFT DOWNFIELD TO READ BACK THEIR TKOF CLRNC. WE ONLY PRESUMED THEY HAD RECEIVED IT EARLIER. SUPPLEMENTAL INFO FROM ACN 271002: THE PROB WE HAD OCCURRED AFTER WE STARTED THE ROLL. WE SEE THE ACFT AND EXPECTED IT TO BE ROTATING IMMEDIATELY AND MAKING A QUICK R TURN. THE SMALLER AND SLOWER DASH 8 WAS NOT OFF THE GND; NOR DID IT TURN WHEN LEAVING THE GND -- WE DECIDED TO STOP OUR TKOF RATHER THAN CHANCE OVERRUNNING THE SLOWER ACFT.