2 SMTS TRIED TO TAKE OFF WITH THE SAME CLRNC.

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I WAS CAPT AND FLYING PLT ON LEARJET ABC. WE WERE DEPARTING WILLOW RUN ARPT; PART 91; TO LOUISVILLE; KY; TO PICK UP FREIGHT. IT WAS RAINING WITH 2.5 MI VISIBILITY. WE WERE CLRED INTO POS ON RWY 23L. MOMENTS LATER WE RECEIVED WHAT WE THOUGHT WAS OUR TKOF CLRNC. THE FO ACKNOWLEDGED THE CLRNC BY SAYING 'ABC CLRED FOR TKOF.' AT ABOUT 100 KTS; WE RECEIVED A CALL FROM TWR 'CANCEL TKOF CLRNC.' I ABORTED THE TKOF. AS WE WERE COMING TO A STOP ON 23L; JUST SHORT OF THE INTXN OF 32; ANOTHER LEARJET WAS ALSO COMING TO A STOP ON 32. I WAS NOT AWARE OF THE OTHER LEARJET IN POS ON 32. APPARENTLY; WHEN THE TKOF CLRNC WAS GIVEN; IT WAS FOR BBB. THE FO THOUGHT IT WAS FOR ABC AND READ BACK THE TKOF CLRNC. HEARING NO RESPONSE FROM TWR; WE HAD NO REASON TO BELIEVE THAT THE CLRNC WAS NOT FOR ABC. PERHAPS OUR ACKNOWLEDGEMENT OF THE CLRNC WAS BLOCKED BY BBB ALSO ACKNOWLEDGING THE SAME CLRNC OR THERE MAY HAVE BEEN SOME PROB WITH CONFUSION BTWN THE 2 NUMBERS. LATER THAT MORNING AT SDF; WE FOLLOWED BBB OUT FOR TKOF AND BOTH TWR AND DEP CTL WERE CONFUSING THE 2 NUMBERS. THE QUICK ACTION OF THE CTLR; AND THE IMMEDIATE RESPONSE OF 2 FLC CREWS; PREVENTED WHAT COULD HAVE BEEN A FATAL ACCIDENT.