ON DODJE ARR TO FTW; FLT CREW OF A DA2000 MISUNDERSTAND D10 CLRNC OF DIRECT CABBY INTXN AS DIRECT CADDY LOM FOR RWY 34. ATC ALERTED CREW OF DEVIATION.

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ARRIVING FTW VIA THE DODJE3 STAR. REGIONAL APCH ISSUED A CLRNC TO 'DIRECT CABBY; THEN HDG 270 DEGS.' WE HAD RECEIVED THE CURRENT ATIS WHICH CALLED FOR LNDG RWY 34 AT FTW. I HAD ENTERED THE APCH INTO THE FMS FOR SITUATIONAL AWARENESS AND BACKUP TO A VISUAL APCH. WHEN ISSUED THE CLRNC TO CABBY; I UNDERSTOOD IT TO BE CADDY; WHICH IS THE FAF FOR RWY 34 AT FTW AND ENTERED 'DIRECT TO' ON THE FMS. ABOUT 3 TO 4 MINS LATER; THE CTLR ASKED OUR HDG; WHICH WAS STILL APPROX 300 DEGS. HE ADVISED WE MISSED OUR TURN AND TO NOW 'TURN TO HDG 250 DEGS.' I GOT ON THE RADIO AND STATED WE HAD NOT YET REACHED CADDY. HE REPLIED; 'YOU'VE PASSED IT BY 10 MILES. TURN L NOW TO 250 DEGS' WHICH WE COMPLIED WITH. WE THEN CAUGHT THE ERROR OF GOING DIRECT TO CADDY; NOT CABBY AS CLRED. I APOLOGIZED FOR THE ERROR TO WHICH THE CTLR RESPONDED 'NO PROB.' WHEN HANDED OFF TO THE NEXT CTLR THE PNF AGAIN APOLOGIZED AND RECEIVED THE SAME RESPONSE. CONTRIBUTING FACTORS WHICH I BELIEVE COMPOUNDED THE SIT 1) HAVING TWO INTXNS WITHIN 30 NM OF EACH OTHER SERVING THE SAME ARPT BEING SO CLOSE TOGETHER IN PRONUNCIATION AND SOUND. A BUSY RADIO ENVIRONMENT WITH ATC TALKING FASTER THAN THE NORMAL MODE OF CONVERSATION; CADDY AND CABBY SOUND IDENTICAL. 2) ON THE EASY AVIONICS/FMS; WHEN A FIX FURTHER DOWN THE RTE IS SELECTED; ALL FIXES IN BETWEEN ARE REMOVED FROM THE WAYPOINT LIST. NOW; WHEN CADDY WAS SELECTED; CABBY WAS REMOVED FROM THE WAYPOINT LIST ON THE INAV SCREEN. WHEN WE HEARD CABBY FROM ATC; IT WAS NOT ON OUR FMS LIST AND THIS CREATED SOME CONFUSION UNTIL THE STAR CHART WAS CONSULTED. STILL BEING NEW TO THE EASY SYSTEM; THIS IS SOMETHING WE'VE NOW LEARNED TO EXPECT AND WILL BE MORE VIGILANT DURING SUBSEQUENT OPS.