What is the difference between aviation "accident" and "incident"?
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
  crew: or
  
  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
  operation.


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.