[p_l]

Accident, Incident and Serious Incident have explicit definitions in civil aviation, and are also graded internally and thus might have different scope of investigation.

A planned landing in terrain, if it caused no injuries but caused enough damage to aircraft to prevent takeoff without repair, would be classified as accident, but its investigation might be very brief depending on the event in question.

Essentially if you have an "occurence", you're required to report it to NTSB, which in turn will grade it and decide if you need even a cursory interview.

[sokoloff]

Not quite correct. You have to report any accident and any of a specific list of serious incidents to the NTSB. You do not have to report other incidents or occurrences.

https://www.law.cornell.edu/cfr/text/49/830.5

Also note: a landing that required repairs would not necessarily be an accident either, assuming no serious injuries occurred. "Engine failure or damage limited to an engine if only one engine fails or is damaged, bent fairings or cowling, dented skin, small punctured holes in the skin or fabric, ground damage to rotor or propeller blades, and damage to landing gear, wheels, tires, flaps, engine accessories, brakes, or wingtips are not considered “substantial damage” for the purpose of this part." (Those minor damages, even if they made the airplane require repairs prior to further flight, are not enough to make that landing an accident.)

[p_l]

Well, I'm going off more ICAO rules than NTSB specific - what I know for sure is that the differences you just specified are prerogative of NTSB and its parent govt to hash out (and seen it being decided upon in Polish PKBWL)