THIS AIRPLANE WAS INVOLVED IN A NEAR COLLISION WITH ANOTHER AIRPLANE WHILE IN POSITIVE CONTROL AIRSPACE. BOTH AIRPLANES TOOK EVASIVE ACTION. VISIBILITY WAS REPORTED BY BOTH FLIGHT CREWS AS BEING REDUCED BY THE PRESENCE OF CIRRUS CLOUDS WITH NO VISIBLE HORIZON. THIS AIRPLANE HAD ACKNOWLEDGED AND RESPONDED TO A TURN INSTRUCTION ISSUED TO A THIRD AIRPLANE WITH A SIMILAR CALL SIGN, AND TURNED TO A HEADING WHICH PUT THE TWO INVOLVED AIRPLANES ON AN INTERSECTING COURSE. THE TURN INSTRUCTION WAS CHALLENGED BY THE AIRPLANE FOR WHOM IT WAS INTENDED, BUT THE INCIDENT AIRPLANE WAS NEVER TURNED BACK TO ITS ORIGINAL HEADING. THE ERROR WAS DISCOVERED A SHORT TIME LATER BY THE MANUAL CONTROLLER AND POINTED OUT TO THE RADAR CONTROLLER. HE ISSUED TURN AND CLIMB INSTRUCTIONS TO THE INCIDENT AIRPLANE ALONG WITH A TRAFFIC ADVISORY. CORRELATION OF THE TWO DFDR READOUTS WITH RADAR TRACK DATA SHOW, THAT AT THE POINT OF CLOSEST APPROACH, VERTICAL SEPARATION WAS BETWEEN 95 AND 200 FT.