FLC OF AN LTT CPR ACFT INADVERTENTLY TKOF ON A CLRNC FOR ANOTHER ACFT RESULTING IN AN NMAC AT INTERSECTING RWYS.

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THE VFR FLT WAS INITIATED AS A FLT TRAINING CHKOUT ON TYPE FOR ANOTHER PLT FROM HOU IN AN SMT. WE TAXIED FROM THE FBO TO RWY 17. WE WERE TOLD TO HOLD SHORT AND WE ACKNOWLEDGED. SHORTLY THEREAFTER; WE WERE INSTRUCTED TO TAXI INTO POS AND HOLD FOR DEPARTING TFC. THE TWR SEEMED TO BE VERY BUSY AT THE TIME AND GAVE DEPARTING ORDERS TO WHAT WE BELIEVE WAS OUR ACFT AND ADVISED THAT WE WERE CLRED FOR 'IMMEDIATE' TKOF. AFTER I HAD ACKNOWLEDGED THAT WE HAD RECEIVED TKOF CLRNC; WE PROCEEDED WITH OUR DEP. ON RWY 22 AT THE SAME TIME; A MEXICAN REGISTERED LTT WAS THE ONE APPARENTLY CLRED FOR THE IMMEDIATE TKOF. SINCE THE TAIL NUMBERS WERE SOMEWHAT SIMILAR IN SOUNDING AND CONSIDERING THE LOUD COCKPIT NOISE OF THE ACFT; WE ASSUMED THAT THE CLRNC WAS FOR US. UPON ACKNOWLEDGEMENT OF OUR CLRNC THE TWR NOT DENYING THAT THE CLRNC WAS NOT FOR US BUT INDEED FOR THE LTT BASICALLY CONFIRMED THAT BOTH OF US IN THE COCKPIT HAD HEARD THE CORRECT CLRNC. UPON REACHING THE INTXN OF RWY 17 AND 22; THE TWR ADVISED US THAT WE HAD PASSED WITHIN TO HIS ESTIMATION; 100 FT FROM EACH OTHER. IMMEDIATELY AFTER WE REALIZED THAT WE HAD PASSED CLOSE TO ANOTHER ACFT THE TWR ADVISED THE LTT FOR AN IMMEDIATE R TURN AND TOLD US THAT WE DID NOT HAVE THE CLRNC FOR TKOF WHICH WAS A TOTAL SURPRISE TO US. I FEEL THIS INCIDENT COULD HAVE BEEN AVOIDED IF THE TWR WOULD HAVE ADVISED US THE 'IMMEDIATE TKOF' WAS NOT FOR OUR ACFT. THE TWR COULD HAVE BEEN WATCHING OUR ACFT TO MAKE SURE WE WERE STILL HOLDING INTO POS AND COULD HAVE ADVISED US TO ABORT TKOF WHEN THEY REALIZED WE WERE ALSO ON TKOF ROLL.