Commercial Fixed Wing
Flight Crew Air Transport Pilot (ATP)
Situational Awareness
Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Issued New Clearance; Flight Crew Returned To Clearance
Procedure; Environment - Non Weather Related; Human Factors
FO was pilot flying and CA PM. Took off XXR at ZZZ on the ZZZZZ X SID. After passing ZZZZZ1; Center inquired which fix we were navigating to next. PM replied with the next fix on the SID. The Controller sounded confused and verified our routing. Both pilots at this point reviewed the clearance versus the filed route and saw the FMS was set up for the ZZZZZ departure instead of the amended ZZZZZ2 departure. The cleared departure has the same 3 initial fixes before heading slightly more southerly to a different transition than the filed departure. The PM queried ATC if a change in course was needed or if additional information would be needed later and ATC said no. ATC then cleared us to a VOR which was on both the filed and cleared flight plan and the flight continued to the destination. CA loaded the FMS while FO was preflighting the aircraft. FO was pilot flying and therefore conducted the pre-start briefing. Neither pilot noticed the amendment on the PDC or corrected the FMS when the briefing was conducted. It was the first leg of a new crew change so that could have contributed to a lack of attention to detail or distraction. Complacency played a part as PDC are not amended frequently from filed routing. FO hadn't flown in a month and didn't notice how an amended clearance on a PDC looks and briefed what was loaded in the FMS. Whoever loads the FMS should double check the clearance and verify the cleared route and have the other pilot verify the fixes more closely against the clearance as some have the same initial fixes.
On the climbout; the FMS was programmed for a departure procedure that led south then north east. The first fix on the departure flown and the correct one ATC wanted were the same. When initial contact with ATC was made; I mentioned we were climbing via the departure that was thought to be correct. After about 8 minutes or so; ATC notifies us that we were off course and queried which departure we were on. We notified ATC and they came back and said we were supposed to be; according to their paperwork on a different departure procedure. ATC cleared us to a fix about 50 miles away and we resumed the flight without incident and without request for contact from ATC. The cause of this event may be contributed to a failure to cross check the programming of the FMS alongside the PDC as opposed to just the release. Suggestion to prevent this include not programming the route in the FMS until after the PDC/clearance has been received from ATC. Including climbing via the XXXXX departure in all initial contacts with departure control when applicable.
Air carrier flight crew reported a track heading deviation.  ATC questioned their routing and the crew realized they had an amended clearance.