RPTR ACFT ON VECTORS WAS CLRED FOR A VISUAL APCH; BUT WHEN RPTR ACFT TURNED INBOUND APCH CTL TOLD THEM THEY WERE FOLLOWING ANOTHER ACFT. WHEN RPTR FLC SAW THEIR TFC ACFT THEY HAD TO TAKE EVASIVE ACTION TO KEEP SEPARATION.

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AFTER A GAR DUE TO WINDSHEAR ON A VISUAL APCH TO RWY 36 AT DCA; MY ACFT WAS VECTORED TO A L DOWNWIND W OF THE ARPT FOR ANOTHER APCH. I WAS ASKED IF I HAD THE RIVER IN SIGHT AND SAID THAT I DID. I WAS CLRED FOR A VISUAL APCH AND STARTED A TURN TO THE E TOWARD THE POTOMAC RIVER AND THE ARPT. WE WERE TOLD WE WOULD FOLLOW A B757 ON A STRAIGHT IN APCH. I EXPECTED THE ACFT TO BE AHEAD OF ME AND PRESENT A WAKE TURB PROB BUT WHEN I FIRST SAW THE B757 IT WAS AT MY 1 O'CLOCK AS I TURNED TOWARD THE E. I TURNED S TO AVOID THE B757. I WAS VECTORED BEHIND 2 OTHER ACFT FOR A LONG STRAIGHT IN AND LANDED WITHOUT FURTHER INCIDENT. I THOUGHT I WAS CLRED FOR A VISUAL APCH BEFORE I ACKNOWLEDGED OR SAW MY TFC. I TURNED IN TO KEEP PACE WITH THE USUAL RUSH OF DCA TFC. THE B757 WAS A COMPANY ACFT AND SOME CALL SIGN CONFUSION MAY HAVE CONTRIBUTED TO THIS SIT. SUPPLEMENTAL INFO FROM ACN 330770: THE COCKPIT WAS VERY BUSY WITH CHKLISTS AND OTHER COCKPIT DUTIES WHEN ALL 3 CREW MEMBERS HEARD ATC ASK IF WE HAD THE RIVER IN SIGHT. THE COPLT RESPONDED AFFIRMATIVE AND WE HEARD ATC CLR US FOR THE VISUAL. I CAN'T BE CERTAIN WHETHER WE HEARD ATC WRONG OR THEY MADE A MISTAKE BUT IMMEDIATELY AFTER TURNING TOWARD THE RIVER WE RECEIVED SIMULTANEOUS WARNINGS FROM ATC AND TCASII ABOUT THE B757 ESTABLISHED ON THE RIVER VISUAL. VISUAL CONTACT WITH THE TFC WAS IMMEDIATE AS WAS A TURN TO THE S WHICH PREVENTED A CONFLICT. REGARDLESS OF WHO MADE THE INITIAL MISTAKE THE SIT MIGHT HAVE BEEN AVOIDED IF BOTH PARTIES LISTENED MORE CAREFULLY TO THE CALL SIGNS GIVEN BY THE OTHER PARTY. WITHOUT LISTENING TO THE TAPES I REALLY CAN'T SAY MUCH ELSE ABOUT THE SIT EXCEPT THAT A BUSY COCKPIT MAY HAVE CONTRIBUTED.