A runway excursion occurs when an aircraft fails to confine its take off or landing to the designated runway.
SKYBRARY, electronic repository of safety data related to ATM, http://www.skybrary.aero/index.php/Runway_Excursion
Types of Runway Excursion
A departing aircraft fails to become airborne or sucessfully reject the take off before reaching the end of the designated runway.
A landing aircraft is unable to stop before the end of the designated runway is reached.
An aircraft taking off, rejecting take off or landing departs the side of the designated runway.
An aircraft attempting a landing touches down in the undershoot area of the designated landing runway within the aerodrome perimeter.
A runway or taxiway other than the designated one is used for a take off or a landing