A BUSINESS JET CREW HAD PROBS GETTING PERMISSION TO FLY FROM ZZZ ARPT AFTER THE PERMISSION WAS SUPPOSEDLY GRANTED BY THE FAA.

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ON NOV/MON/01 WE FLEW A TRIP FROM ZZZ1-ZZZ. A FEW DAYS PRIOR OUR DISPATCH REQUESTED AND RECEIVED AN ARO FOR THE TRIP. ON DAY OF THE FLT WE RECEIVED OUR IFR CLRNC AND DEPARTED FOR ZZZ. WE WERE VECTORED TO INTERCEPT THE ILS XA AND RECEIVED CLRNC TO LAND ON RWY XB. AFTER LNDG WE TAXIED TO THE RAMP. APPROX 1 HR AND 10 MINS LATER WE WERE CLRED TO TAXI TO RWY XC. WE WERE THEN CLRED INTO POS AND HOLD. IN POS WE WERE ASKED TO STATE OUR TYPE; WE TOLD THEM WE WERE A CHALLENGER. THE CTLR THEN ASKED IF WE WERE TN; AND WE ASKED HIM TO REPEAT THE QUESTION; AFTER HE DID WE REPLIED THAT NO WE WERE AN N. WE WERE THEN REQUESTED TO CLR THE RWY AND WE RETURNED TO THE RAMP. AFTER APPROX 10 MINS WE WERE TOLD TO CONTACT TWR ON THE PHONE. WE TRIED SEVERAL TIMES; BUT ONLY GOT BUSY SIGNALS. WE CONTACTED GND AND TOLD THEM OUR TROUBLE IN CONTACTING THE TWR. WE WERE ADVISED THAT THEY WERE WORKING ON CLRING US FOR DEP AND TOLD TO CALL GND WHEN READY TO TAXI. WE WERE GIVEN CLRNC TO TAXI AND CLRED FOR TKOF ON RWY XC. AFTER DEP AND ONCE AT ALT ON OUR WAY TO OUR DEST (ZZZ2); WE CALLED THE TWR PHONE NUMBER AND SPOKE WITH THE TWR SUPVR. HE TOLD US THAT THERE WAS A LOT OF CONFUSION AND MULTIPLE LISTS THEY HAD TO DEAL WITH. HE TOLD US WE WERE THE SEVENTH ACFT THAT DAY THAT THIS SIT HAS HAPPENED TO. HE ALSO TOLD US THAT THIS WAS NOT GOING ANY FURTHER. THE PROB AROSE BY MY MISINTERPRETATION OF THE FDC NOTAM. ALSO THE ABILITY TO SECURE AN ARO AND A CLRNC. THE MISUNDERSTANDING WAS ALSO DONE BY SEVERAL OTHERS IN OUR DEPARTMENT. TO KEEP THIS FROM HAPPENING AGAIN WOULD REQUIRE MAKING THE NOTAM EASIER TO READ AND INTERPRET. ALSO; CHANGE THE ARO REQUEST SYSTEM TO HELP CATCH ANY MISTAKES; AND FINALLY NOT TO ISSUE CLRNCS TO THE ACFT.