In airline parlance, the OOOI rule is the best one to remember:

Out = Pushed back from gate (when brakes are released. Doesn't mean the plane actually moves exactly at this time away from the gate). On united.com, it will say "Departed Gate" when this happens.

Off = Flight takes off (wheels leaves the ground). On united.com, it will say "In Flight" when this happens.

On = Flight lands (wheels touch the ground). On united.com, it will say "Landing/Taxiing to Gate" when this happens.

In = Flight arrives at the gate (parking brake is set. This does not mean that the jetbridge has been connected to the fuselage and that the doors are open). On united.com, it will say "Arrived" when this happens.

Hope that clarifies!