CAPT OF A B737 BECAME CONFUSED AS TO WHAT TAXI RTE TO USE IN TURNING OFF AT THE END OF THE RWY AFTER LNDG CAUSING TWR INTERVENTION TO CORRECT HIS RWY DEP. THE COMMERCIAL ARPT CHART INDICATED ACCESS OFF THE END OF THE RWY WHICH HE BELIEVED TO BE AVAILABLE SO HE WOULD NOT HAVE TO TAXI ONTO AN ADJACENT INTERSECTING RWY.

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LNDG ON RWY 10R AT CMH. PLANNED ON LONG ROLLOUT TO TURN OFF CLOSER TO ASSIGNED GATE. MISSED TXWY TO GATE. ROLLED TO RWY END. BEGAN TO TURN OFF BUT NOTICED IT WAS ACTIVE RWY 23/5. SINCE I WAS NOT CLRED TO TAXI ONTO ACTIVE RWY AND THERE WAS AN ACFT ON FINAL BEHIND ME; I OPTED TO TAXI ONTO WHAT I THOUGHT WAS A DISPLACED THRESHOLD AND THEN OFF THE RWY ON A TXWY LOCATED AT THE END OF THE DISPLACED THRESHOLD. I LATER FOUND OUT THIS IS A REPOSITIONED RWY END LINE. AFTER I HAD TAXIED ABOUT 20-30 FT ONTO THE OVERRUN; THE TWR ASKED ME WHY I HAD RUN OFF THE RWY. THE COMMERCIAL 10-7 CHART SHOWS THIS AREA AS AN ACTIVE TXWY. THE TWR THEN CLRED ME FOR A 180 DEG TURN AND OFF THE RWY AT THE RWY 23/5 JUNCTION. FATIGUE -- OVER 8 HRS FLYING FIRST DAY AFTER SHORT LAYOVER. UNFAMILIAR -- OVER A YR SINCE I HAD BEEN AT CMH. TRYING TO BE TOO SAFE NOT TURNING ONTO ACTIVE RWY. I DID NOT REALIZE I HAD DONE ANYTHING WRONG UNTIL THE TWR ASKED ME WHY I RAN OFF THE RWY. IN FACT; I'M STILL NOT SURE I DID ANYTHING WRONG SINCE THE AREA IS DEPICTED AS AN ACTIVE TXWY. UP UNTIL ABOUT 2 YRS AGO; THIS AREA WAS USED AS PART OF THE RWY.