FLC OF AN ACR LGT BELIEVED A CALL FROM THE TWR TO CLR THE RWY WAS FOR THEM AND THEY ABORTED TKOF.

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WE WERE DEPARTING DCA FOR ATL ON ACR X WHEN WE WERE INVOLVED IN A VERY CONFUSING SIT THAT RESULTED IN AN ABORTED TKOF (BY US) AND A GAR (BY ACR Y FLT) AT CURFEW TIME IN DCA. ALL WAS NORMAL UNTIL THE POINT WHERE ACR X WAS CLRED INTO POS RWY 36 FROM TXWY C TO BE READY FOR AN IMMEDIATE TKOF. AN ACFT HAD JUST LANDED (ACR Z) AND AN ACR Y FLT WAS ON A 4 1/2 MI FINAL. THE NEXT COM WAS A QUERY BY DCA TWR TO THE LNDG ACFT AS TO MAKING THE NEXT TURNOFF AND AN AFFIRMATIVE REPLY FOLLOWED BY 'ACR X; CLRED FOR TKOF.' AS I PREPARED TO START THE TKOF AND LOOKING TO MY FO TO VERIFY THE CALL SIGN AND TKOF CLRNC; THERE WAS AN URGENT CALL FROM DCA TWR; 'ACR X; CLR THE RWY.' AT THAT POINT; THERE WERE TOO MANY QUESTIONS IN MY MIND TO CONTINUE THE TKOF; AND THE URGENCY OF THE CALL DID NOT LEAVE ROOM FOR QUESTIONS. I EXITED THE RWY AT TXWY A; NOSE TO NOSE WITH A SMALL PVT JET. AT THAT POINT; TWR SENT THE ACR Y FLT AROUND AND SORTED OUT THE GND SIT. HE EXPLAINED TO US THAT THE LNDG (ACR Z) HAD STOPPED ON THE RWY AND THE ACR X; CLR THE RWY CALL WAS FOR HIM. IN RETROSPECT; I STILL COULD NOT HAVE TAKEN OFF EVEN THOUGH I THOUGH THAT THE LNDG ACFT WAS CLR OF THE RWY. THE ACR X PREFIX TO OUR TKOF CLRNC RAISED THE QUESTION OF ACR Y ACFT ON RWY 03 AND AN ERROR ON MY PART IN TAKING RWY 36. THAT; COUPLED WITH THE ACR X CLR THE RWY CALL LED TO A VERY CONFUSING SIT. DCA TWR WAS SIMPLY TRYING TO MOVE TFC EFFICIENTLY BUT WHEN THE LNDG ACFT WAS SLOW TO EXIT HE USED IMPROPER AND INCOMPLETE CALL SIGN VERBIAGE WHICH LEFT US UNSURE OF WHOM HE WAS ADDRESSING.