HDG TRACK DEV IN THIS WRONG RWY APCH.

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LNDG ILS 31R; VISUAL APCHS 31L; ARR PUSH. TRAINING DEVELOPMENTAL ON LCL CTL. ACR LGT X CHKS IN; 15 MI FINAL; SAYS HE WAS ISSUED VISUAL TO 31L; WHEN HE WAS ISSUED AN ILS TO 31R. HE IS MOVING PAST ILS 31R APCH COURSE AND CLOSING ON COMPANY ACFT Y ON VISUAL APCH TO 31L. LGT X ASKS; 'WHERE IS THIS ACFT Y GOING'? I TOOK THE FREQ FROM THE TRAINEE; ESTABLISHED VISUAL SEPARATION BTWN THE ACFT (I WAS NOT TALKING TO ACFT Y FOR 31L) AND HAD LGT X BEGIN A MISSED APCH (HDG 270). AFTER COORD WITH APCH CTL; LGT X WAS ISSUED 270 HDG; 7000 FT AND A FREQ FOR RESEQUENCING. APCH ATTEMPTED TO BRING HIM BACK IN IMMEDIATELY RESULTING IN X BEING IN CONFLICT WITH YET ANOTHER COMPANY LGT Z. VISUAL SEPARATION WAS ESTABLISHED BY APCH AND ALL ACFT LANDED SAFETY. SUGGESTIONS: PAY ATTN TO READBACKS; ESPECIALLY WHEN TRAINING SOMEONE ELSE. APCH CTL WAS ALSO TRAINING. 31L SAVES THIS ACR CONSIDERABLE TAXI TIME; AND THE PLTS HAVE COME TO EXPECT IT. IT IS IMPORTANT FOR THEM TO REALIZE THAT IT IS NOT ALWAYS AVAILABLE; AND THEY SHOULD ALSO PAY MORE ATTN TO INSTRUCTIONS AND READBACKS. SUPPLEMENTAL INFO FROM ACN 187948: WHEN THE CREW TUNED THE FINAL CTLR'S FREQ; THEY FOUND THE FREQ VERY CONGESTED AND THE CTLR ISSUING A NON- STOP BARRAGE OF INSTRUCTIONS TO MANY DIFFERENT ACFT. HIS SPIEL WAS CONTINUALLY INTERRUPTED BY THE SQUEAL OF SIMULTANEOUS TRANSMISSIONS. FOR ABOUT 2 MINS THE CREW COULD NOT BREAK IN; BUT FINALLY THE CTLR CALLED THE ACFT AND GAVE A HDG CHANGE TO 060 DEG AND INSTRUCTED THE CREW TO LOOK FOR AN ADV TECH AT 12 O'CLOCK AND FOLLOW THAT ACFT TO THE ARPT. THE RWY TO BE USED WAS NOT SPECIFIED; NOR WAS THE ASSIGNED ALT AND SPD CHANGED. THE FO WAS FLYING AND THE CAPT WAS WORKING THE RADIO. AS THE CAPT LOOKED AT 12 O'CLOCK HE SAW AN ADV TECH WDB ABOUT 5 MI AHEAD IN A R TURN. IT WAS VISIBLE IN THE HAZE ONLY BECAUSE BOTH ITS WINGS AND FUSELAGE WERE EXPOSED. THE CAPT ACKNOWLEDGED VISUAL CONTACT WITH THE WDB AND THE FO BEGAN TO SLOW THE ACFT. AT THIS POINT; NEITHER THE ARPT; NOR THE S SHORE OF LONG ISLAND WERE VISIBLE YET; SO VISUAL OPS WERE BEING CONDUCTED IN WHAT WAS ESSENTIALLY AN IFR ENVIRONMENT. AS THE ACFT SLOWED THROUGH 220 KTS; THE CAPT NOTICED THE ILS COURSE BAR MOVE RAPIDLY FROM THE SIDE TO THE CENTER OF THE COURSE INST; INDICATING THAT THE ACFT WAS XING THE 31L LOC. THE CAPT IMMEDIATELY CALLED THE CTLR AND ASKED IF THEY WERE BEING 'TAKEN THROUGH'; AS THE CREW WAS STILL 'INST-APCH' ORIENTED. THE CTLR REPLIED; 'TURN L 290 DEG; MAINTAIN 2000 UNTIL ESTABLISHED; CLRED FOR APCH; CONTACT TWR 119.1'. AGAIN THE RWY WAS NOT SPECIFIED; ALTHOUGH THE CREW WAS NOW LED TO BELIEVE THEY HAD BEEN CLRED TO INTERCEPT THE 31L ILS. AS THE ACFT ROLLED OUT ON FINAL WITH THE ARPT STILL NOT IN SIGHT THE CAPT REALIZED THAT HE COULD NOT SEE THE WDB HE WAS SUPPOSED TO FOLLOW; BUT HE SAW EMERGING FROM THE HAZE TO THE L ANOTHER ACFT Y IN A L TURN TO JOIN THE LOC. THIS NEW ACFT WAS ONLY ABOUT 1 1/2 MI AHEAD AND AT THE SAME ALT. IT WAS OBVIOUS SOMETHING WAS WRONG! THE CAPT CALLED JFK TWR AND ASKED WHERE THE ACFT JUST AHEAD WAS GOING. THE TWR RESPONDED BY ASKING IF THE WDB WAS IN SIGHT. THE CAPT SAID; 'NO; BUT WE HAVE AN LGT ACFT Y JUST AHEAD'. THE TWR THEN ASKED WHAT RWY THE CREW WAS MAKING THEIR APCH TO; AND THE CAPT REPLIED '31L'. THE TWR THEN SAID THE ACFT Y AHEAD WAS A VISUAL TO 31L AND GAVE INSTRUCTIONS TO FLY 270 DEG AND MAINTAIN 2000 FT. ONLY AT THIS POINT DID THE CREW REALIZE THEIR ERROR. THEY HAD ASSUMED THEY WERE CLRED FOR AN APCH TO 31L WHEN THEY HAD BEEN IN FACT VECTORED FOR 31R. THE CTLR ERRED BY NOT SPECIFYING THE RWY TO BE USED. AND THE CAPT ERRED BY ACKNOWLEDGING CONTACT WITH THE WDB WHICH TO THE CTLR IMPLIED THE ABILITY TO COMPLETE A VISUAL APCH AND THE ASSUMPTION OF ACFT SEPARATION OBLIGATIONS. BUT THE UNDERLYING FAULT WHICH CONTRIBUTED TO THESE ERRORS WAS THE CHAOS OF THE COMS FREQ. WHEN A FREQ IS SATURATED AND MORE AND MORE INSTRUCTIONS HAVE TO BE ISSUED TO MORE AND MORE ACFT; THE TENDENCY IS TO OMIT REQUIRED TRANSMISSIONS; SHORTEN PHRASES; OMIT READBACKS AND MAKE ASSUMPTIONS ABOUT PLTS' AND CTLRS' INTENTIONS. THESE COM DISCIPLINE LAPSES LEAD TO INCIDENTS. LUCKILY; THIS INCIDENT RESULTED IN NO NEAR MISS; NO EVASIVE ACTION; AND NO DISCOMFORT TO THE PAX ON EITHER PLANE. SMALL SCREW-UPS LIKE THIS HAPPEN ALL DAY LONG IN THE NEW YORK TCA. BUT ANY ONE OF THOSE INCIDENTS CAN START A SNOWBALL REACTION WHICH CAN QUICKLY OVERWHELM THE SYS'S CAPABILITY TO COPE; SINCE COM-WISE; IT'S ALREADY OVERLOADED. IN THIS DAY AND AGE; ACFT NEED DATA LINK LIKE ACARS.