Background
The captain of a Boeing 737 reported a brief delay at the gate due to a cargo issue. The automatic terminal information service indicated that departures were using runway 34R, with the option of taking the full length or an intersection at taxiway Q.
Taxi Events
Ground control cleared the flight to taxi to runway 34R at taxiway Q. During the taxi, the first officer (FO) was occupied with discussions with dispatch and completing flight paperwork, while the captain taxied the aircraft and handled all air traffic control (ATC) communications. As the airplane approached taxiway Q, the flight crew received an amended flight release. The captain then switched to the local control frequency, where he heard the local controller issue a clearance to taxi into position and hold on runway 34C. The captain read back the clearance, including the phrase "runway 34 center."
Departure
While the FO was finishing preflight activities, the local controller cleared the flight for takeoff from runway 34C, noting traffic on short final. The captain again repeated the clearance for takeoff on "runway 34 center." However, the captain aligned the airplane on the runway 34R centerline and then transferred control to the FO. The aircraft departed without incident. The local controller observed the airplane taking off from runway 34C and did not issue an abort order because there were no potential traffic conflicts.