Incident can refer to any event – big or small, good or bad, intentional or unintentional. A bank robbery, a funny or controversial situation, an argument between celebrities, etc. – all can be described as incidents.
An accident is a bad event caused by error or by chance. Accidents are always unintentional, and they usually result in some damage or injury. A car crash is one example of an accident. If some equipment malfunctions in a factory and injures the workers, that is also an accident. Examples of the minor accidents are when you step on someone’s foot or spill your coffee on someone else. You didn’t want or plan to do it.
All accidents can ALSO be described as incidents – but NOT all incidents are accidents.
If a drunk driver runs his car into a group of people, that is an accident (he did not intend to do it; it was caused by alcohol and chance). It could also be described as an incident (“The incident occurred on Main Street at around 2:30 AM”).
If three people were arrested after fighting in a bar, that is an incident (but not an accident – because the fight was not by chance; they intended to fight).