RPTED SIT IN WHICH THE GND CTLR CLRED THE WRONG ACFT TO CROSS THE ACTIVE RWY WHILE AN ACFT WAS ON TKOF ROLL.

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AFTER LNDG ROLLOUT ON RWY 12L; WE WERE SWITCHED TO GND CTL AND TOLD TO HOLD SHORT OF RWY 12R (WE WERE ON TXWY R). AFTER A MIN OR SO WE WERE TOLD TO BE READY TO EXPEDITE ACROSS. AT THIS POINT BOTH MY FO AND I LOOKED TO THE R AND SAW AN ACFT ON 2-3 MI FINAL AND ANOTHER ACFT WHICH APPEARED TO BE ROLLING OUT. WE ACKNOWLEDGED THIS INFO AND BOTH OF US ASSUMED THAT WHEN THE ACFT ROLLING OUT SLOWED SUFFICIENTLY TO EXIT THE RWY WE WOULD BE INSTRUCTED TO EXPEDITE ACROSS THE RWY. WE WERE SO INSTRUCTED. 1/4 OF THE WAY ACROSS; GND CTL ASKED IF WE COULD HOLD SHORT (ABOUT THE SAME TIME WE REALIZED THAT THE ACFT WE THOUGHT WAS IN THE LNDG ROLLOUT WAS IN THE CLB RIGHT AFTER TKOF). WE ESTIMATE HE LIFTED OFF THE RWY APPROX 3000 FT FROM OUR POS AND PROBABLY CLRED OUR ACFT BY ABOUT 500 FT. FROM CONVERSATION WITH THE TWR SUPVR LATER; THERE WAS ANOTHER FLT HOLDING SHORT OF RWY 12R AT TXWY E TO TKOF ON RWY 12L AND GND CLRED US ACROSS FIRST INSTEAD OF HIM. A RECOMMENDATION: STL USES DIFFERENT TWR FREQS FOR RWY 12R & L. WHEN ONE LANDS ON RWY 12L THEY USUALLY TELL YOU TO HOLD SHORT OF TXWY P; THE PARALLEL TXWY AND CONTACT GND. GND THEN COORDINATES XING RWY 12R. I BELIEVE IT WOULD BE MUCH SAFER IF GND SWITCHED US TO THE RWY 12R TWR FREQ FOR XING SO WE COULD HEAR WHAT IS GOING ON PRIOR TO XING.