These are the NTSB definitions of incident and accident

Accidents

In Part 830, the NTSB defines an accident as:

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 and when all such passengers have disembarked,
in which any person suffers death or serious injury,
in which the aircraft receives substantial damage.
Substantial damage means damage or failure which adversely affects the structural strength, performance, or flight characteristics of the aircraft. This type of damage would normally require major repair or replacement of the affected component.

There are certain items that are not considered “substantial damage” by the NTSB. These include:

Engine failure or damage limited to an engine if only one engine fails or is damaged
Bent fairings or cowling
Dented aircraft skin or small punctured holes in the skin or fabric
Ground damage to rotor or propeller blades
Damage to landing gear, wheels, tires, flaps, engine accessories, brakes, or wingtips
Incidents

The NTSB defines an incident as an occurrence other than an accident, associated with the operation of an aircraft, which affects or could affect the safety of operations. While many incidents do not need to be reported to the NTSB, there are serious incidents that must be reported.

Operators should review the full list of reportable incidents, but the following are a few common examples:

Damage to property, other than the aircraft, estimated to exceed $25,000 for repair (including rials and labor) of fair market value in the event of total loss, whichever is less
In-flight fire
Flight control system malfunction or failure
Complete loss of information, excluding flickering, from more than 50% of an aircraft’s electronic cockpit displays, such as EFIS
ACAS resolution advisory issued when an aircraft is being operated under an IFR flight plan and compliance with the advisory is necessary to avoid a collision, or if the aircraft is operating in Class A airspace

I would say that if no damage was done then it's not an incident. However, a common question will be have you ever failed a check ride or stage check. Answer truthfully. Flying in the 135 world I promise you I have flown with people have had far worse problems and are flying today.