Confusion; Situational Awareness; Communication Breakdown
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Issued New Clearance; Air Traffic Control Issued Advisory / Alert; Air Traffic Control Separated Traffic; Flight Crew Became Reoriented; Flight Crew Requested ATC Assistance / Clarification
Chart Or Publication; Human Factors
A normal takeoff clearance was received. After airborne Tower cleared us direct to FEZTR. At about 6;000 ft. Tower handed us off to Departure. Departure assigned us a heading stating; 'you're way off course.' The Captain; as Pilot Monitoring; replied that Tower gave us direct FEZTR. Eventually Departure cleared us to another fix down line and own nav on course. The Tower gave us a late handoff and told us to go direct to FEZTR. After the confusing check on with Departure Control we both agreed that it was odd to be cleared to a down line fix by Tower. And it was odd that Tower kept us on frequency so long. And it was odd that Departure knew nothing about it. We had a rider in the jumpseat listening in and we all agreed that we heard the clearance to FEZTR. We could have asked Tower for a handoff sooner. We could have questioned Tower's instruction to go direct FEZTR; but we thought Tower and Departure control were jointly monitoring/coordinating our progress reference some other traffic. On check in with Departure Control; we said we were climbing via the departure; but it would have been more clear to highlight the non standard situation by stating we were proceeding direct FEZTR per Tower's direction.
[Report narrative contained no additional information.]
Air Carrier flight crew reported Tower issued a clearance to a fix and Departure Control did not know about it.