C525 DEP FROM RNO INITIATES WRONG DIRECTION TURN AND EXPERIENCED CONFLICT WITH B737.

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OUR IFR CLRNC WAS AS FOLLOWS: CLRED TO JOHN WAYNE ARPT VIA THE RENO 3 DEP; RADAR VECTORS TO FRIANT VOR AS FILED 15000 FT; 119.2; XXXX ON THE SQUAWK. AS WE WERE TAXIING TO RWY 16L WE RECEIVED AN AMENDMENT TO OUR CLRNC FROM GND CTL. DEPART RENO MUSTANG 6 DEP AS FILED 10000 FT; THE REST REMAINS UNCHANGED. AFTER CLRED FOR TKOF; WE FLEW 3 DME OFF THE LOC AND STARTED OUR L-HAND TURN TO FMG; THE AUTOPLT WAS ENGAGED AND THE HDG BUG WAS USED TO START THE TURN TOWARDS FMG VOR. THE NAV WAS THEN ENGAGED AND AUTOPLT CONTINUED THE TURN TO FMG VOR. THE DEP CTLR THEN CLRED US TO 15000 FT. APPROX WITHIN A FEW MI OF FMG VOR; DEP CTL SAID 'TURN TO THE L TO A HDG OF 160 DEGS.' I THEN SELECTED THE HDG MODE AND BEGAN TURNING THE HDG BUG TO THE L FOR A HDG OF 160 DEGS. THE HDG BUG AT THAT TIME WAS TO THE R OF THE DIRECTIONAL CTL; SO THE AIRPLANE INITIALLY STARTED A TURN TO THE R. I IMMEDIATELY CORRECTED THE HDG BUG AS QUICKLY AS POSSIBLE. AT THIS TIME WE THOUGHT THE CTLR WAS GIVING US A HDG FOR OUR ON-COURSE DIRECTION. THE CTLR THEN TOLD US TO CONTACT HIS SUPVR FOR A POSSIBLE DEV ERROR. AT THIS TIME WE WERE UNDER THE IMPRESSION THE CTLR THOUGHT WE WERE PERFORMING THE WRONG DEP AND THAT IT WAS SIMPLY A MISUNDERSTANDING. MY PARTNER CONTACTED THE SUPVR ONCE WE WERE ON THE GND IN SNA. TO THE BEST OF MY KNOWLEDGE OF THAT CONVERSATION; THE SUPVR SAID THAT THERE WAS AN AIRLINE FLT ALSO NAVING TO THE FMG VOR ON AN ARR AND RECEIVED A TCASII WARNING; BUT DID NOT HAVE TO TAKE EVASIVE ACTION. WE NEVER GOT A WARNING ON OUR TCASII THAT WAS ON AND FUNCTIONAL. THE DEP CTLR DID NOT INFORM US OF THE TFC. THE R TURN WAS INADVERTENT AND NOT DELIBERATE. I WAS IN FULL UNDERSTANDING OF THE CTLR'S INSTRUCTIONS AND MADE THE APPROPRIATE CORRECTIVE ACTIONS.