ACR X NON ADHERENCE TO ATC CLRNC LANDED WRONG RWY. RWY INCURSION.

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ACR X HEADING 200 DEGS ON A R DOWNWIND AND CLRED FOR THE VISUAL APCH TO RWY 2L AT NASHVILLE. APPROPRIATE IRS FREQ WAS SELECTED FOR RWY 2L. APCH AND LNDG WERE MADE ON RWY 2C. WE COMMENTED TO EACH OTHER THAT THE GS WAS IN ERROR AND CONTINUED VISUALLY (TURNED OFF ILS AT THAT POINT.) I REALIZED THE MISTAKE ON LNDG ROLLOUT WHEN I WAS LOOKING FOR THE T2 TXWY TO TURN OFF ON AND SAW S5. RWY 2C EXTENDS OUT APPROX 1 MI FURTHER TO THE S; I SAW THE R SIDE AND WENT R AFTER THE CTR RWY. HAD I LOOKED AT THE 10-9 ARPT DIAGRAM MORE CLOSELY THE PROB WAS AVERTED. BNA TWR WAS CALLED AFTER ARR AT THE GATE. HE SAID THEY HAD NO TFC SO THERE WAS NO PROB. SUPPLEMENTAL INFO FROM ACN 296420: ILS FREQ FOR RWY 2L WAS TUNED AND IDENTED; BOTH PF AND MYSELF THOUGHT IT WAS UNUSUAL GS INDICATOR SHOWED THE FLT ON GS AND THE VASI'S SHOWED THE FLT HIGH ON GS. THE COARSE DISPLACEMENT WAS NOT IN EITHER PLT'S XCHK ON GS INDICATOR. UPON TOUCHDOWN AND TAXIING OFF THE RWY; WAS IT DISCOVERED THE FLT HAD LANDED ON RWY 2C INSTEAD OF RWY 2L. AS THE PNF I WOULD HAVE HOPED; SINCE I CONSIDER ATC PART OF COCKPIT RESOURCE MGMNT; THAT TWR WOULD HAVE NOTICED OUR DISCREPANCY AND INFORMED THE FLT.