I have, in a previous career incarnation, organised a survey of numerous airlines asking them about their operating definitions, in order to arrive at industry 'guidelines' rather than standards.
Basically, it's up to the individual airline - there is no standard definition, but among the major airlines at least it is almost inevitably the start of pushback. I have however known some carriers to use 'aircraft moving under its own power' and 'doors closed'.
Equally, each airline has its own definition of 'on-time'. The commonest standard is two minutes, but I have known zero, three, four, five, ten and fifteen (the latter was a purely longhaul airline).
If you want a really grey area, ask an airline what is meant by 'scheduled' in 'scheduled time of departure'.