CTLR TRAINING IN PROGRESS ACR X HAD LTSS WITH ACR Y AND NMAC WITH CPR Z. SYS ERROR.

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ACR X WAS ESTABLISHED VIA RADAR VECTORS ON R DOWNWIND FOR RWY 1R AT 3000 FT. ALL OTHER ACFT WERE ASSIGNED A SPD EXCEPT US. AT APPROX 3 MI FROM FIELD; WE WERE ASSIGNED 2000 FT. AT 6-7 MI; WE WERE ASSIGNED A R TURN TO HDG 300 DEGS. WE WERE NOT OFFERED AN EXPLANATION (I.E.; VECTORS BASE LEG; ETC); AND IT WAS CLR THAT THIS HDG AND ALT WOULD CONFLICT WITH A HVY ACR Y PRECEDING US. I HAD NO IDEA AS TO THE INTENT OF THE CTLR AT THIS POINT. AS IT BECAME MORE EVIDENT THAT OUR HDG ALT WOULD CONFLICT WITH ACR Y; WE WERE INSTRUCTED TO ACCELERATE; AND Y WAS SLOWED TO 150 KTS AND GIVEN 'S-TURNS.' STILL NOT KNOWING ATC'S INTENTIONS; WE REMAINED ON OUR LAST ASSIGNED HDG OF 300 DEGS. NEXT XMISSION FROM ATC INFORMED US THAT WE HAD BEEN CLRED FOR A VISUAL APCH TO RWY 1L; AND TO PROCEED TO RWY 1L AND CONTACT TWR. AFTER CHKING IN WITH TWR WE DISCOVERED THAT WE WERE DIRECTLY BELOW A BUSINESS JET Z (CITATION?) WHO WAS NOT VISIBLE TO US IN OUR TURN; AND HAD ALSO BEEN CLRED ON A VISUAL APCH TO RWY 1L. (ON INITIAL CONTACT WITH TWR; THEY WERE OBVIOUSLY SHOCKED THAT WE WERE LINED UP FOR THE L RWY.) AS WE WERE AT A LOWER ALT; WE WERE CLRED TO LAND; AND THE Z JET WAS SENT AROUND. WE COMPLETED OUR VISUAL APCH TO RWY 1L; AND LANDED WITHOUT FURTHER INCIDENT. I WOULD ESTIMATE THAT OUR LATERAL SEPARATION Y WAS LESS THAN 2 SM; AND THAT OUR VERT SEPARATION WITH THE Z WAS APPROX 500 FT. A SUBSEQUENT PHONE CONVERSATION BTWN THE CAPT AND ATC REVEALED THAT CTLR TRAINING WAS IN PROGRESS.