There are indeed only two 'official' classifications of aviation incidents, which are defined in ICAO Annex 13.
Accident. An occurrence associated with the operation of an aircraft
which takes place between the time any person boards the aircraft with
the intention of flight until such time as all such persons have
disembarked, in which:
a) a person is fatally or seriously injured as a result of
being in the aircraft, or
direct contact with any part of the aircraft, including parts which have become detached from the aircraft, or
direct exposure to jet blast,
except when the injuries are from natural causes, self inflicted or
inflicted by other persons, or when the injuries are to stowaways
hiding outside the areas normally available to the passengers and
b) the aircraft sustains damage or structural failure which:
adversely affects the structural strength, performance or flight characteristics of the aircraft, and
would normally require major repair or replacement of the affected component,
except for engine failure or damage. when the damage is limited to the
engine, its cowlings or accessories: or for damage limited to
propellers, wing tips, antennas, tires, brakes, fairings, small dents
or puncture holes in the aircraft skin: or
c) the aircraft is missing or is completely inaccessible.
Note I.-- For statistical uniformity only, an injury resulting in
death within thirty days of the date of the accident is classified as
a fatal injury by ICAO.
Note 2.-- An aircraft is considered to be missing when the official
search has been terminated and the wreckage has not been located.
And then there is
Incident. An occurrence, other than an accident, associated with the
operation of an aircraft which affects or could affect the safety of
They do also define 'serious incident', but simply as an incident which was nearly an accident; which is still an 'incident' by the definition above.