B350 DEP FROM BHM TAXIED ONTO RWY WITHOUT ATC CLRNC.

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I WAS TO RELOCATE A B350 FROM THE BIRMINGHAM ARPT TO SHELBY COUNTY ARPT; 20 MI S OF BIRMINGHAM. ON LEAVING THE FBO; A DEP CLRNC WAS RECEIVED ALONG WITH TAXI INSTRUCTIONS. INSTRUCTED TO TAXI TO RWY 18 WITH HOLD SHORT OF RWY 24; WHICH I DID. LATER; CLRNC WAS GIVEN TO CROSS RWY 24 WITH HOLD SHORT RWY 18. ON THIS FLT; WAS AN EXPERIENCED OBSERVER IN MAKE AND MODEL OF ACFT. WITH THE HELP OF THIS OBSERVER; WE COMPLETED THE BEFORE TKOF FLT CHKS AND SYS RUN-UPS. ALONG WITH THIS RUN-UP WERE SOME POINTERS ON USING THE FMS. DURING THESE CHKS; WE BELIEVED THAT WE WERE INSTRUCTED BY ATC TO TAXI INTO POS ON RWY 18. UPON STOPPING ON RWY 18; ATC INSTRUCTED US TO IMMEDIATELY EXIT RWY 18 AND THEN LATER REISSUED US A TKOF CLRNC. I WAS DISTRACTED DURING THE SYS CHK AND THE POINTERS ON THE EFIS/FMS. THE PREVENTION IS TO VERIFY CLRNCS WHEN NOT 100% SURE OF ATC'S INTENT. SUPPLEMENTAL INFO FROM ACN 618322: WE WERE CLRED TO TAXI AND HOLD SHORT OF RWY 24. WE WERE SUBSEQUENTLY CLRED ACROSS RWY 24 TO HOLD SHORT OF RWY 18. AFTER XING RWY 24; GND CTL INSTRUCTED US TO CONTACT THE TWR. AFTER CONTACTING TWR IT WAS THE UNDERSTANDING IN THE COCKPIT THAT WE WERE CLRED ONTO RWY 18. TWR TOLD US TO EXIT THE RWY IMMEDIATELY. AFTER ANOTHER AIRPLANE LANDED; WE WERE CLRED FOR TKOF. I AM UNSURE OF THE EXACT INSTRUCTIONS FROM THE TWR.