For the airline (and passengers that want to make their flight) departure time is when the door is to be closed. There is more time built into the schedule for pushback, taxi, etc. So if you have an 8:00 flight and the door closes at exactly 8:00, you departed on-time even if you sit in the penalty box for an hour.

Flight aware tracks the actual wheels up time. If you want to know how long it took to get from the gate to takeoff, use the airline website to find departure time, then flight aware to get takeoff time. The difference is pushback, taxi, hold, etc.