A SINGLE PLT OPERATED C550 JET BECAME CONFUSED AS TO ATC INSTRUCTIONS DEPARTING FROM TEB RESULTING IN A TRACK DEV.

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TETERBORO CLRNC GAVE ME A STANDARD SID CALLED TETERBORO 4. THEN CALLED BACK AND GAVE ME A VFR DEP; BUT WITH SPECIFIC INSTRUCTIONS. THEY WERE TO FLY OFF RWY 19 INTERCEPT THE 235 DEG RADIAL FROM TEB; THEN TURN TO 280 DEGS; CONTACT DEP. WHEN I CONTACTED DEP; HE ASKED ME WHAT MY HEADING WAS. I TOLD HIM 270 DEGS. HE SAID THAT I WAS SUPPOSED TO BE ON A 290 DEG HDG. THEN HE GAVE ME A 360 DEG HDG FOR ABOUT 3 MINS THEN CLRED ME TO MY FIRST FIX COYTE INTXN. WHEN I PUT THE COYTE INTXN INTO MY FMS THE GPS FAILED MOMENTARILY; AND WHEN IT CAME BACK ON LINE THE AUTOPLT TURNED THE AIRPLANE BACK TO TEB TO A 060 DEG HDG. BY THE TIME I CAUGHT IT; IT WAS TOO LATE; NY CAME BACK VERY ANGRY; GAVE SOMEONE VECTORS AND SENT ME BACK TO COYTE INTXN. THE REASON I DID NOT CATCH THE AUTOPLT AND GPS PROB WAS THAT I WAS VERY CONFUSED AS TO THE CLRNC AND ATC'S ACTIONS. SO I WAS LOOKING AT THE TUTORIAL FOR THE TETERBORO 4 SID. NONE OF WHAT MY CLRNC HAD SAID; AND NONE OF WHICH ATC TOLD ME WERE CONSISTENT WITH ANY PUBLISHED DEP FROM TEB.