FLT CREW OF B763 INADVERTENTLY FLEW SID OTHER THAN THAT CLRED.

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THE FO WAS FLYING THE ACFT. DURING INITIAL CLB; HE VERBALIZED THAT THE FMS MAP DISPLAY (MAGENTA LINE) DID NOT AGREE WITH THE DEP CLRNC (BIBOS 2D) FROM RWY 7. I WAS INVOLVED WITH FREQ AND ALT CHANGES AND TOLD HIM TO FLY THE DEP VIA MANUAL BACKUP. HE SELECTED MANUAL VOR; BUT BEGAN TO INCORRECTLY NAV VIA THE BIBOS ZE DEP TRANSITION. SOON AFTER; THE CTLR ASKED US TO VERIFY OUR CLRNC -- I RESPONDED THAT IT WAS THE BIBOS ZD. HE STATED THAT WE WERE NOT FLYING IT PROPERLY. I CONFIRMED (VIA THE CHART AND FMS DISPLAY) THAT WE WERE L OF THE CORRECT RADIAL AND DIRECTED THE FO TO STEER BACK TO THE R TO RE-ESTABLISH. THE DEP CTLR THEN CLRED US DIRECT TO A DOWNLINE DEP (SID) INTXN ON THE BIBOS 2D. THERE WAS NO APPARENT TFC CONFLICT NOTED AT ANY TIME. THE PROPER DEP SID HAD BEEN BRIEFED BTWN ALL 3 CREW MEMBERS PRIOR TO BOTH THE PUSHBACK AND TKOF. (IT WAS NOTED THAT IT WAS A CHANGE FROM THE BIBOS ZG INDICATED ON THE FLT PLAN). AFTER THE OCCURRENCE; THE FO INDICATED THAT HE WAS ACTUALLY THINKING OF THE BIBOS ZE. THERE WERE SEVERAL DISTRS DURING THE BRIEFING THAT LIKELY CONTRIBUTED TO THE CONFUSION. A CHANGE TO AN EARLIER SLOT TIME BY ATC; DISCUSSION OF DEICING DUE TO VERY LIGHT SNOW FLURRIES; PRESSURE TO PUSH AWAY FROM THE GATE BY OPS PERSONNEL; AND ULTIMATELY TKOF CLRNC BEFORE THE UPDATED SLOT TIME. HOWEVER; I DID VISUALLY CONFIRM THAT THE PROPER DEP WAS LOADED IN THE FMS AND DID COMPARE THE LEGS PAGE INFO WITH THE SID. I WAS CERTAIN OF THE EXPECTED RTE. HUMAN FACTORS CONSIDERATIONS -- THE FO WAS APPARENTLY UNSURE OF THE DEP PROC; BUT DID NOT SO INDICATE. I DEFERRED TO HIM DURING CLB IN PART BECAUSE HE SOUNDED SO CERTAIN. (I AM RELATIVELY NEW TO INTL OPS -- HE HAD MORE EXPERIENCE IN THE ARENA OF OPS). THE RELIEF PLT FAILED TO FOLLOW THE DEP PROC EVEN THOUGH HE HAD THE CHART IN HAND -- HE OFFERED NO ASSISTANCE. THE CTLR COULD HAVE OFFERED AN INITIAL VECTOR RATHER THAN TO ALLOW US TO DEV FARTHER AWAY FROM PROPER COURSE. I WILL NOT AGAIN PUSH AWAY FROM THE GATE UNLESS I HAVE CONFIRMATION FROM EACH CREW MEMBER THAT WE ARE CONFIDENT OF THE INTENDED FLT PATH.