A B737 FLT CREW MISUNDERSTOOD THEIR CLRNC AND SWITCHED TO THE WRONG FREQ RESULTING IN XING A RWY WITHOUT A CLRNC.

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AFTER RECEIVING A TAXI CLRNC; WE TAXIED OUT TO RWY 31C. THE CLRNC READ; 'FLT NUMBER; TAXI TO RWY 31C VIA TXWY P AND TXWY G. YOU ARE CLRED TO CROSS RWY 31L.' WHEN WE GOT ONTO TXWY G; MY FO SWITCHED RADIO #1 TO TWR. WE THOUGHT IT WAS TWR. IT WAS 118.4 DEP. IN THE PROCESS; I PROCEEDED TO TAXI ALL THE WAY TO THE EASTERN MOST LINE WHERE THERE WAS ANOTHER COMPANY JET IN LINE TO TAKE OFF. ALL 3 LINES WERE OCCUPIED. ABOUT THE TIME WE GOT THE TAIL OF THE COMPANY JET; I NOTICED A CITATION LNDG ON RWY 31R. THAT WAS WHEN WE NOTICED WE HAD THE #1 RADIO ON 118.4. WE THEN SWITCHED TO 118.7 AND TWR SAID NOTHING TO US. WE WERE THEN INSTRUCTED POS AND HOLD AND TWR SAID; 'IN THE FUTURE; HOLD SHORT OF RWY 31R ON TXWY G.' WE ROGERED THAT AND NEVER HEARD ANY MORE. THE CITATION DID CONTINUE TO LAND AND WE MUST NOT HAVE BEEN THAT CLOSE TO RWY 31R; EXCEPT WE WERE OVER THAT HOLD SHORT LINE. I TREATED THE EASTERNMOST LANE AS I WOULD IF I WOULD HAVE TAXIED OUT OF THE OLD TERMINAL AND PULLED RIGHT INTO IT. NEVER AGAIN WILL I TAKE A CLRNC TO CROSS ONCE AS A CLRNC TO CROSS AGAIN.