HIO Local Controller describes a NMAC where an aircraft is told to follow an aircraft type on final; while there are two of the same type of aircraft on final. Downwind traffic turns in to follow wrong aircraft.

Narrative

Aircraft X was IFR and released from P80. I told the aircraft cleared for takeoff. Aircraft Y was on final and I cleared it for a touch and go with a wake turbulence cautionary. I told Aircraft Z who was on final too that he was number 2 on final and cleared touch and go. Aircraft A called me on the left downwind and I told the pilot 'Aircraft A; number three; follow Cessna three mile final; runway 31 cleared to land.' Aircraft A replied; 'Follow Cessna; clear to land three one.' I then made other transmissions to other aircraft and then scanned for Aircraft A to make sure it had turned base. I saw the aircraft on base but was not sure if he was going to follow Aircraft Z mainly because of the visibility. In the background there were dark clouds and it was hard to spot some of the airplanes and also judge distances. I asked Aircraft A if he had the Cessna ahead and to his right on final in sight because at that moment I thought he was in a base turn that would cut off Aircraft Z. He said he had the Cessna in sight but I did not know if he was referring to Aircraft Z or Aircraft Y who was short final. I told Aircraft Z to turn left so that he would turn away from the final; but instead Aircraft A took evasive action and climbed the aircraft to avoid hitting Aircraft Z. That's when Aircraft Z said on frequency that he wanted to report that. I told Aircraft A to proceed northbound and then I told him to head towards the airport and he was cleared to land. He landed safely. I don't have any recommendations. I thought when I gave Aircraft A his sequence and clearance to land he knew which aircraft to follow.