ACR MADE SIDESTEP MANEUVER TO PARALLEL RWY IN IMC WX CONDITION.

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ATIS GAVE LNDG RWY AS 14. APCH CTL THEN SWITCHED THIS TO 27L DURING VECTORS. A BRIEFING WAS DONE IN COCKPIT ON THIS APCH AND WE TURNED FINAL TO 27L AFTER BEING CLRED FOR APCH TO 27 LEFT. INSIDE OM CTLR SAID WE WERE MAKING APCH TO WRONG RWY AND WERE SUPPOSED TO BE MAKING APCH TO 27 RIGHT. AT THE TIME THIS OCCURRED WE HAD DOWNWIND VISIBILITY TO THE GND BUT NOT ENOUGH FORWARD VISIBILITY TO SEE THE END OF 27 RIGHT. WE WERE TOLD TO TURN 30 DEG TO RIGHT AND LAND ON 27 RIGHT. THE END OF THE RWY AND RWY ENVIRONMENT WAS PICKED UP AND A NORMAL LNDG OCCURRED. AFTER THE LNDG I CONFIRMED WITH THE OTHER TWO PLTS THAT WE HAD BEEN GIVEN 27 LEFT FOR APCH. A DANGEROUS SITUATION COULD HAVE OCCURRED DURING THE CONFUSION. NEITHER THE CAPT OR COPLT HAD APCH PLATES OUR FOR 27 RIGHT. THE ONLY OTHER COURSE OF ACTION WOULD HAVE BEEN TO TAKE A MISSED APCH AND IF I HAD NOT SEEN THE 27 RIGHT ENVIRONMENT WOULD HAVE DONE SO. SOMEWHERE WE FELT THAT A SWITCH IN CTLRS WAS MADE AND THE WORD WAS NOT PASSED PROPERLY AS TO WHICH APCH WE WERE MAKING.