ACR X MADE APCH TO WRONG RWY HAD LTSS FROM ACR Y. PLTDEV.

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ACR X WAS ON RADAR VECTORS TO DTW FOR RWY 21L ILS. CAPT (PNF) WAS VISUALLY FOLLOWING ARR ACFT IN SEQUENCE FOR LNDG. FO WAS MANUALLY FLYING ACFT. ON TURNING BASE LEG ON VECTORS; CAPT SPOTTED ACR Y IN THE TURN FROM THE OPPOSITE SIDE; AND MADE THE COMMENT THAT ACR Y WILL BE GOING TO THE R SIDE. ON THE FINAL INTERCEPT VECTOR THE CAPT NOTICED THE ACR Y ROLLING OUT ON SAME HDG WITH OUR ACFT DIRECTLY BEHIND IT. CAPT ASKED DTW TWR WHAT ACR Y WHO WAS NOW 2-3 MI AHEAD AND 1300 FT BELOW (TCASII EQUIP) WAS DOING. WHEN INFORMED HE WAS GOING TO RWY 21R; THE CAPT LOOKED DOWN AT THE FO'S NAV RECEIVER AND FOUND IT TUNED TO RWY 21R. TWR GAVE US A 360 DEG VECTOR FOR SPACING AND AN UNEVENTFUL LNDG ON RWY 21L. FACTORS. CAPT NAV WAS STILL SET TO DTW VOR TO GIVE FO DME CAPABILITY. ACFT WAS STILL IN FLAPS 5 DEG MODE AND RECHK OF NAVAIDS ARE MADE ON FLAPS 15 DEG LNDG CHK. CAPT WAS OUTSIDE OBSERVING TFC WHILE FO WAS BUSY INSIDE MANUALLY FLYING ACFT. FO THOUGHT WE WERE GOING TO THE R SIDE EVEN THOUGH ALL INSTRUCTIONS AND BRIEFS WERE TO THE L SIDE. CORRECTIVE ACTION. CAPT NAV SHOULD HAVE BEEN TURNED TO LOC FREQ EARLIER. WOULD HAVE CAUGHT GOING THROUGH RWY 21L LOC IN THE TURN. NO MENTION OF THE ACR Y TFC BY APCH ONLY MLG TFC THAT WAS AHEAD OF US. DOUBLECHK NAV'S PRIOR TO TURN TO INTERCEPT. WHILE IT IS IMPORTANT TO KEEP AN EYE ON; WHAT'S GOING ON OUTSIDE IN HVY TFC; ALSO YOU MUST RECHK YOUR PARTNER AND INSIDE.