FLC OF A DC9-30 LINED UP WITH THE WRONG PARALLEL RWY RESULTING IN APCH CTLR INTERVENTION TO PROVIDE THEM WITH THE LOC FREQ FOR THE ASSIGNED PARALLEL RWY TO WHICH THEY BELIEVED THAT THEY WERE HEADED.

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APCH CTL ISSUED ILS RWY 28R AND VECTORED US TO FINAL APCH CTLR. HE DSNDED US TO 3000 FT AND GAVE US AN INTERCEPT HDG AND ISSUED APCH CLRNC. I INTERCEPTED LOC AND TURNED INBOUND. THE CTLR SAID IT APPEARED WE WERE INTERCEPTING ILS RWY 28R WHICH WE WERE. HE INDICATED WE SHOULD BE ON APCH FOR ILS RWY 28L. HE THEY ISSUED US THE ILS FREQ 111.7 FOR ILS RWY 28R. WE ASKED HIM IF WE SHOULD BREAK OFF THE APCH AND HE ISSUED US A CLRNC FOR ILS RWY 28R THEN. WE WERE BEING VECTORED FOR R DOWNWIND WHICH IS USUAL FOR ILS RWY 28R; WHICH GAVE US MORE VERIFICATION FOR THE ILS RWY 28R. THE FINAL CTLR MAY HAVE THOUGHT WE WERE ISSUED AND EXPECTED RWY 28L; WHICH I DO NOT BELIEVE WE WERE. THERE WERE NO CONFLICTS. THERE WERE SNOW SQUALLS OVER THE AREA. I THINK MAYBE A MISUNDERSTANDING BTWN THE 2 APCH CTLRS DEVELOPED AS THERE WAS A HEARBACK AND READBACK FROM THEM EVERY TIME. THIS THING HAPPENS AND IN A HIGH TFC AREA WITH REDUCED VISIBILITY IT IS VERY IMPORTANT FOR THE CTLR AND PLT TO GET GOOD COMS ON IDENT OF THE RWY TO LAND ON. MAYBE A PROC FOR THE FINAL CTLR TO RENAME THE ILS AND GET A FINAL READBACK CLRNC FROM THE PLT PRIOR TO THE FINAL INTERCEPT HDG IS GIVEN; AND THE FINAL ILS CLRNC IS ISSUED. THE PLT WOULD THEN BE GIVEN A SECOND CHANCE TO CORRECT ANY ERROR THAT MIGHT EXIST.