MD80 FLC MAKES APCH TO WRONG RWY. THEY HAD MISSED THE CLRNC FOR ASSIGNMENT TO ANOTHER RWY DURING CLRNC DIRECT TO VOR. PIC WAS LATER INFORMED THAT TRAINING WAS IN PROGRESS FOR AN APCH CTLR. EVENT DETECTED BY ACR Y BEHIND ACR X.

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DURING APCH TO DEN LNDG RWY 35L/R INITIALLY ASSIGNED RWY 35L. ABOUT 13 MI APCHING FROM SE GIVEN 270 DEG HDG AND TOLD TO CHANGE FREQ. ON CONTACT CLRED DIRECT TO FALCON VOR. MUCH RADIO TFC DELAYED OUR CALL OF RWY IN SIGHT WHEN ABLE WE CALLED IN SIGHT AND WERE CLRED VISUAL TO RWY 35L WE THOUGHT. ON LINE UP ON RWY 35L FLT ABOVE AND BEHIND ASKED APCH IF WE WERE LINED UP ON HIS RWY. WE WERE THEN CLRED TO LAND RWY 35R AND DID SO WITHOUT FURTHER EVENT. AFTER LNDG TALKED TO APCH ON PHONE AND THEY SAID NO CONFLICT BECAUSE OF ALT SEPARATION. THEY SAID CHANGE OF ASSIGNMENT OCCURRED ON NEW FREQ WHEN GIVEN DIRECT FALCON VOR NEITHER OF US CAUGHT THE CHANGE. IT MIGHT HAVE HELPED IF IT HAD BEEN NOTED AS A CHANGE. WE SHOULD HAVE CAUGHT THE FINAL CLRNC TERMINOLOGY IN ANY CASE. SUPPLEMENTAL INFO FROM ACN 368579: TWR CLRED US TO LAND AND ADVISED OF TFC FOR PARALLEL RWY (WHICH WE ASSUMED WAS RWY 34 SINCE WE HAD A VISUAL ON THAT TFC TO RWY 34). ON GND; CAPT CALLED TWR WHO SAID THAT TRAINING WAS IN PROGRESS BUT THAT WE HAD BEEN CLRED FOR RWY 35R.