C501 INBOUND TO VGT EXPERIENCED CONFUSION WITH STAR DEPICTION AND ATC INTERP.

Narrative

I WAS ON AN IFR FLT PLAN TO FLY FROM GOFFS (GFS) TO CLARR THEN 'CLARR ONE ARR' TO N LAS VEGAS (VGT). ON ARR AT CLARR I TURNED TO JOIN THE 031 DEG HEADING TO SKEBR; 7 MI AHEAD. I WAS CORRECTING TO SKEBR ON L AT 0.1 MI FROM SKEBR TO STAY ON 031 DEG HDG OVER SKEBR. THE LAS VEGAS APCH CTLR ASKED ME IF I WAS 'IN A L TURN?' AND I ANSWERED THAT I WAS OVER SKEBR. SINCE I HAD NOT HEARD ANY RADAR VECTOR GIVEN; I CONTINUED ON A 031 DEG HEADING FOR ANOTHER FEW SECONDS OR MINS AT 13000 FT AND 210 KIAS. THE LAS VEGAS CTLR DIRECTED ME TO TURN L IMMEDIATELY TO A 330 DEG HDG; WHICH I DID. THE LAS VEGAS CTLR THEN WANTED TO KNOW WHY I HADN'T TURNED L EARLIER; AND I TOLD HIM THAT I HAD RECEIVED NO DEGREE TO TURN TO WITH THE EARLIER QUESTION OF WAS I 'IN A L TURN?' I BELIEVE THE LAS VEGAS CTLR WAS CONFUSED OR MIXED UP AND THOUGHT I WAS GOING TO LAS VEGAS MCCARREN (LAS) AND NOT TO N LAS VEGAS (VGT) WHICH I HAD FILED AS MY DEST. THE LAS VEGAS CTLR THEN DIRECTED ME TO CALL WHEN I GOT ON THE GND. AFTER I LANDED I CALLED AND WAS TOLD THIS WAS LAS VEGAS TRACON. I WAITED AND A SUPVR CAME TO THE PHONE. I EXPLAINED THAT I HAD APCHED SKEBR IN A SLIGHT (10 DEGS) L TURN AND DID NOT UNDERSTAND THE CTLR WANTED ME ON A SPECIFIC HEADING IN THE L TURN. I DID NOT HEAR OR ACKNOWLEDGE A SPECIFIC DEG HEADING AND MY COPLT DID NOT HEAR A SPECIFIC DEG HEADING. I DID TURN L IMMEDIATELY WHEN THE CTLR TOLD ME TO TURN L IMMEDIATELY TO 330 DEGS. THE SUPVR INFORMED ME THAT I HAD READ THE CLARR ONE ARR WRONG AND THAT FROM SKEBR I SHOULD HAVE TURNED L TO 345 DEGS. I RESPONDED THAT I THOUGHT IT WAS RADAR VECTORS FROM SKEBR TO N LAS VEGAS. I ALSO STATED THAT IF I WAS WRONG I WAS SORRY AND I 'WOULD NEVER DO IT AGAIN.' SUPVR SAID; 'THAT'S ALL I WANTED TO HEAR.' I WENT BACK TO MY PLANE AND LOOKED AT THE 'CLARR ONE ARR' AGAIN; AS THIS HAD BEEN MY FIRST TIME HAVING FLOWN THIS APCH FROM GOFFS (GFS). MY PLATE CLRLY INDICATES AT SKEBR IN A BOX; 'N LAS VEGAS AFTER SKEBR INTXN EXPECT RADAR VECTORS TO ARPT.' THIS IS A CLR MISCOM ON MY PART AND ON THE PART OF THE LAS VEGAS APCH CTLR. I DID NOT CLARIFY HIS QUESTION OF MY BEING 'IN A L TURN?' I SHOULD HAVE ASKED FOR A SPECIFIC HEADING AND I DID NOT BECAUSE I WAS WAITING FOR HIM TO GIVE ME A RADAR VECTOR AFTER SKEBR ON THE 031 DEG RADIAL. THE LAS VEGAS APCH CTLR MIGHT HAVE THOUGHT THAT I WAS LNDG AT MCCARREN (LAS) WHICH REQUIRES A L TURN TO 345 DEG HDG TO ISSAR. WE SHOULD HAVE CONFIRMED EARLIER THAT I WAS FILED AND PLANNED TO LAND AT N LAS VEGAS (VGT). BECAUSE OF THIS MISCOM; I WAS HEADED INTO THE DEP AREA FOR MCCARREN (LAS); A VERY BUSY ARPT. I WILL ENDEAVOR TO ALWAYS CONFIRM MY COMS WITH A READBACK WHEN APCHING A LARGE BUSY ARPT IN ORDER TO MINIMIZE MISCOM.