C210 PLT TAXIED PAST THE RWY END LIGHTS; ONTO AN ACTIVE TXWY.

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AFTER LNDG ON RWY 36 AT OMA; TWR INSTRUCTED ME TO TAXI MY C206 TO THE RAMP BY MAKING A R TURN ON TXWY C; L TURN ON RWY 32R; R TURN AT THE END; AND THEN CONTACT GND. I LOOKED AT THE ARPT DIAGRAM FOR THE ROUTING AND CONTINUED TO TAXI AS INSTRUCTED. AS I APCHED THE END OF THE RWY; AND CROSSED PAST THE RED RWY END LIGHTS/WHITE LINE ON THE END OF THE RWY; TWR IMMEDIATELY INSTRUCTED ME TO STOP. AFTER STATING THAT I WAS TOLD TO MAKE A R AT THE END WHICH WAS TXWY Y; AND INSTRUCTING ME TO MAKE A 180 DEG TURN AND TAXI ONTO TXWY Y; TWR SWITCHED ME TO GND. GND INSTRUCTED ME TO TAXI TO THE RAMP AND CONTACT THE TWR. AFTER SHUTTING DOWN THE ACFT; I CALLED THE TWR AS INSTRUCTED. TWR 'DISCUSSED' THE SIT WITH ME. ATC ADVISED ME THAT THE RED LIGHTS AT THE RWY; AND THE WHITE LINE; MEANT STOP. HE ADDED THAT THE R TURN INSTRUCTED AT THE BEGINNING OF THE TAXI CLRNC MEANT TO TURN R ONTO TXWY Y. HE MENTIONED THAT WHEN I CONTINUED PAST THE END OF RWY 32R; I WAS; HOWEVER; ON AN ACTIVE TXWY (TXWY U). AFTER A BIT MORE CONVERSATION; CLARIFICATION; AND 'EDIFICATION;' THE CALL ENDED WITHOUT FURTHER ACTION BY TWR. I RECEIVED AND PROCESSED ALL THE INPUT RECEIVED FROM TWR/GND AND PERCEIVED ATC TO BE HELPFUL AND PROFESSIONAL. THE CONFUSION THAT CAUSED THIS INCIDENT; IN ESSENCE; WAS THE CLRNC TO TAXI TO THE END ON RWY 32R WITH A R TURN AT THE END. LOOKING AT THE ARPT DIAGRAM; IT INITIALLY SEEMED THE END WAS WHERE TXWY B WAS LOCATED. CONTRIBUTING TO THIS PROB WAS THE APPROX 1.8 HR FLT MISSION IN VERY TURBULENT AIR AND WINDS BTWN 20-30 KTS; THE FACT THAT MY PAX HAD 'BECOME SICK' AT THE VERY END OF THE FLT DUE TO THE TURB; THE HIGH WINDS ON THE GND; NIGHTTIME; A RELATIVELY UNFAMILIAR AIRFIELD; AND THAT THE TAXI CLRNC DID NOT STATE TO 'TURN ONTO TXWY Y' BUT TAXI TO THE END OF RWY 32R AND THEN A R TURN AT THE END; ALL PROBABLY CONTRIBUTED TO THE ANOMALY. IN THIS SIT; TAXI TO THE END I GUESS TO ME SEEMED TO THE END OF THE TAXI RTE INSTRUCTIONS WITH THE R TURN ON THE TXWY AT THE END; WHICH WAS TXWY B. TWR IMMEDIATELY STOPPED ME AS I WAS PASSING THE END OF THE RWY; WHICH SEEMED THEY WERE WATCHING ME THE WHOLE WAY. NO RWY INCURSION OCCURRED INTO RWY 36; BUT THE TWR DID AID IN PREVENTING AN OCCURRENCE WITH STOPPING MY TAXI AND CORRECTING/REROUTING MY TAXI RTE.