G4 FLT CREW IS INSTRUCTED TO FLY 010 DEG HDG AFTER DEP BY TWR CTLR. FLT CREW COMPLIES AND DEP CTLR INDICATES THAT THEY FLEW THE WRONG HDG.

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WE WERE DEPARTING RWY 31C. WE WERE GIVEN THE DEP SID (VECTOR). JUST PRIOR TO TKOF; THE TWR CTLR TOLD US TO FLY A 010 DEG HDG AFTER DEP. BOTH THE PF AND THE PNF ACKNOWLEDGED VERBALLY TO EACH OTHER THAT AFTER DEP A 010 DEG HDG WAS TO BE FLOWN. THE PNF READ THE CLRNC BACK TO TWR; 'ROGER; AFTER DEP FLY HDG 010 DEGS.' DETAILS OF THE DEP AS PERTAINS TO THE EVENTS STATED HERE: CHART FORMAT. 1) THE SID STATES THAT FOR RWY 31C -- CLB RWY HDG TO 1300 FT BEFORE TURNING ON COURSE. 2) THERE IS ALSO A NOTE ON THE SID -- ALL ACFT EXPECT RADAR VECTORS TO FIRST ENRTE FIX. 3) DME EQUIPPED ACFT -- COMPLETE INITIALLY ASSIGNED TURN WITHIN 4 DME OF THE ARPT. 4) ON THE PICTORIAL IT STATES EXPECT RADAR VECTORS TO FIRST ENRTE FIX. AFTER DEP WE CLBED TO 1300 FT; TURNED TO A HDG OF 010 DEGS AND LEVELED OFF AT 3000 FT. WE WERE FLYING THE HDG WE WERE TOLD TO FLY. WE ALSO MADE OUR TURN TO 010 DEGS WITHIN 4 DME. WE WERE COMPLYING WITH THE SID. WE WERE EXPECTING VECTORS TO OUR FIRST ENRTE FIX. WHEN WE WERE HANDED OFF TO DEP CTL THE CTLR TOLD US THAT WE 'BUSTED THE SID' AND GAVE US AN IMMEDIATE TURN TO 130 DEGS. IT'S POSSIBLE THAT THE TWR CTLR GAVE US THE WRONG HDG TO FLY AFTER DEP. EITHER THAT; OR THE FLT CREW TOTALLY MISUNDERSTOOD THE TWR INSTRUCTIONS.