Well, I know what an in-flight departure is (stimulating is one word for it). But how is 'departure time' defined for airline ops?

Not takeoff, I'm sure, but presumably some point before that. Is it boarding gate closed, doors closed, engine start, push back, ATC clearance to taxy, what?

And is it the same definition for all airports/operators/countries?

I suppose the same question could be asked about 'arrival'.

Just curious.

It varies depending on the airline.

Usually for airlines/aircraft that use ACARS, the 'brakes released' time is used as the departure time (so regardless of whether or not it was held on stand for 10mins due to aircraft taxiing behind, it departed on time).

For the majority of other airlines who don't use ACARS, the departure time is when the wheels start to roll (or when engines are started if the APU is inop and an ASU is required).

Flight times (that pax see) usually have taxi time at both ends incorporated in to them. So an "on time" departure is usually when the brakes are released, or in some cases when the doors are closed.

As others have said it totally depends on the airline concerned. Some I have come across use brakes off, another uses anti-collision light on. Another has the ACARS set to record departure when the front wheels move 3 rotations forward (this stops the dispatcher trying to avoid a delay by asking the captain to release the brakes before the door is even closed). It is down to how the operator wants to fudge the figures to make their on time departure figures look good.