EMB120 CREW HAD A HIGH SPD ABORT WHEN A MOONEY TAXIED ACROSS THE TKOF RWY AT ILM.

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HOLDING SHORT RWY 24 ILS; WE NOTICED SEVERAL VFR/GA ACFT HAD RECENTLY LANDED AND SEVERAL MORE IN TFC PATTERN. THE MOONEY WHO HAD LANDED JUST PRIOR TO OUR DEP REQUESTED R TURN ON RWY 17 (FROM RWY 24) AND TWR APPROVED THE TURN AND CLRED ACFT Y (M20) TO TAXI TO FBO AS HE CLRED US (ACR X) POS AND HOLD ON RWY 24. WHEN ACFT Y (M20) WAS CLR; ILM TWR CLRED US FOR TKOF 'RWY HDG; 10000 FT.' I WAS PF AND CALLED FOR APPROPRIATE CHKLIST. AT THIS POINT WE DID NOT HEAR ANY FURTHER TAXI INSTRUCTIONS FOR THE M20. WE COMMENCED OUR TKOF ROLL. AS WE BEGAN OUR ROLL; WE SAW THE MOONEY TAXIING TOWARD RWY 24. IT SOON BECAME CLR THAT ACFT Y WAS NOT GOING TO HOLD SHORT OF RWY 24. SIMULTANEOUSLY; WE ABORTED THE TKOF AT APPROX 105 KIAS AND TWR CANCELED OUR TKOF CLRNC DUE TO ACFT ON THE RWY (OUR V1 = 111 KIAS). WE WERE ABLE TO ABORT AND EXIT RWY 24 AT RWY 17/35. WE THEN COMPLETED ALL PERTINENT CHKLISTS AND TAXIED BACK TO RWY 24 FOR DEP. PRIOR TO THE HDOF FROM TWR TO DEP; ILM TWR REQUESTED US TO CONTACT THE TWR SUPVR UPON OUR ARR IN ATL. WHEN WE ARRIVED IN ATL; I CALLED THE TWR SUPVR AND HE EXPLAINED THAT THERE WAS A MISCOM BTWN TWR AND ACFT Y. AFTER THE M20 CLRED RWY 24; HE WAS CLRED TO THE FBO; BUT TWR DIDN'T KNOW THAT THE FBO HE WAS GOING TO REQUIRE THE M20 TO CROSS RWY 24 TO GET TO IT; AND WHEN ACFT GOT TAXI CLRNC; HE DID NOT VERIFY THAT HE WAS CLRED TO CROSS THE ACTIVE RWY 24. THE SUPVR ADVISED ME THAT HE HAD SPOKEN WITH THE PLT OF ACFT Y AND WITH THE TWR CTLR. HE EXPRESSED A LACK OF COM CAUSED BY A LACK OF USE OF STANDARD PHRASEOLOGY AND HIGH WORKLOAD OF THE CTLR WORKING ALL LCL FREQS AND HIGH VOLUME OF TFC IN THE AREA. HE ALSO EXPRESSED HIS DEEPEST APOLOGIES.