A B737-300 TAKES POS AND HOLD ON RWY 28L WHEN THE CLRNC WAS FOR A HAWKER WITH A SIMILAR ALPHA NUMERIC AT CMH; OH.

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AS WE APCHED #1 (RWY HOLD LINE) FOR RWY 28L AT CMH; WE SWITCHED FROM GND CTL TO TWR FREQ. NO OTHER ACFT WERE BTWN OUR POS AND THE END OF THE RWY. WE HEARD CMH TWR SAY 'YXX CLRED FOR TKOF; RWY 28L.' WE RESPONDED TO THE CALL BY SAYING 'ACR YXX CLRED FOR TKOF;' TAXIED ONTO THE RWY AND COMPLETED REQUIRED CHKLIST ITEMS. AFTER VISUALLY CLRING FINAL APCH TO THE RWY; WE DIRECTED OUR ATTN DOWN THE RWY AND SAW A HAWKER PULL ONTO THE RWY FROM AN INTXN IN FRONT OF US. WE CALLED; 'TWR ACR YXX' AND BEGAN TO EXIT THE RWY. TWR REPLIED 'YXX; WHAT ARE YOU DOING?' WE RESPONDED THAT WE HAD ACKNOWLEDGED OUR TKOF CLRNC. TWR SAID WE HAD NOT BEEN CLRED FOR TKOF AND THAT WE COULD JUST STAY WHERE WE WERE. WE REPOSITIONED THE ACFT FOR TKOF; REQUESTED A PHONE NUMBER TO DISCUSS THE MATTER AFTER WE ARRIVED AT OUR DEST AND REACCOMPLISHED REQUIRED CHKLIST ITEMS IN PREPARATION FOR DEP. UPON DISCUSSION WITH THE CMH TWR SUPVR; THE CAPT WAS TOLD THE TAPES REVEALED THE FOLLOWING: WE HAD MISTAKEN 'HAWKER YX' FOR 'ACR YXX.' THE CTLR HAD NEVER MENTIONED THE INTXN TKOF IN THE TKOF CLRNC. OUR 'ACR YXX CLRED FOR TKOF' RESPONSE WAS AUDIBLE BUT THERE WAS NO RESPONSE FROM TWR. TO PREVENT RECURRENCE; PROPER TERMINOLOGY SHOULD ALWAYS BE USED TO INCLUDE FULL CALL SIGN AND INTXN DESIGNATION IF TKOF CLRNC IS BEING ISSUED FROM OTHER THAN THE END OF THE RWY. IF AN INCORRECT READBACK (OR ACKNOWLEDGEMENT) OF A CLRNC IS HEARD IMMEDIATE ACTION SHOULD BE TAKEN TO CLARIFY THE SIT.