CORPORATE FLC MISINTERPRETS TA AND POS AND HOLD CLRNC AND DEPARTS WITHOUT TKOF CLRNC.

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HAVING RECEIVED WHAT WAS INTERPRETED AS A VFR TA OF TFC LOW OFF THE DEP END OF RWY 13L AND TKOF CLRNC; TFC IN SIGHT WAS COMMUNICATED AND TKOF BEGUN. AFTER LIFTOFF TWR ADVISED CLRNC HAD NOT BEEN GRANTED BUT POS AND HOLD ONLY; TFC WAS AGAIN CALLED OUT AND WAS STILL INSIGHT AND NOT A FACTOR. NORMAL DEP WAS ACCOMPLISHED WITH NO EFFECT ON ANY OTHER OPS. THIS INCIDENT OCCURRED ON THE FINAL LEG OF A 7 STOP 8 LEG TRIP WITH EXTENSIVE DUTY TIME FOLLOWING A SIMILAR DUTY DAY THE PREVIOUS DAY WITH MINIMAL CREW REST. MISUNDERSTANDING MAY OCCUR AT ANY TIME BUT SHOULD BE CLARIFIED AS WAS NOT DONE IN THIS CASE. TWR ADVISED NO PROB; HOWEVER; IT MUST BE NOTED THE PRESSURES OF CORPORATE AVIATION AND HIGHER DUTY ALLOWANCES CONTRIBUTE TO MISTAKES OF THIS NATURE; UNTIL FLT DEPTS INDUSTRY WIDE DEMAND ADHERENCE TO DUTY LIMITATIONS AND THE FAA REDUCES FLT HR LIMITS AND INCREASES REST PROVISIONS FOR CREW MEMBERS THIS WILL REMAIN A SAFETY ISSUE IN CORPORATE AND REGIONAL OPS. THIS HAS REAFFIRMED IN MY OWN CONDUCT OF FLT OPS THE NEED FOR CONSTANT AWARENESS AND CLR COMS BOTH BTWN COCKPIT AND ATC AND CREW MEMBERS. FORTUNATELY IN THIS INSTANCE; THERE WAS NO HAZARD TO SAFETY BUT THE POSSIBILITY EXISTED. ANY FORUM TO DISCUSS FATIGUE AND COM CLARITY WOULD BE OF HELP TO US ALL; FLT PERSONNEL AND ATC.