From a mathematical perspective,
In an entity-event-state model,
- occurrence describes the instances of either a state or event, either as stochastic or non-stochastic instances.
- incidence describes specifically the occurrence of a state or event encountered by an entity or class of entity, where the occurrence allows a measure of stochastic expectation.
For preamble, let us say that the set Marine Vessel, besides having many other members, has the following members
- Submarine
- Warship
- Tugboat
Submarine is a class of Marine Vessel. Warship is a class of Marine Vessel. Destroyer warship is a class of Warship.
The Delhi is a class of Destroyer warship. The Delhi class itself is not an existence of a ship, but a design of a class of warships. There are three instances of The Delhi in the Indian Navy.
The INS Mumbai is the occurrence of the state of existence (or an instance) of the The Delhi class.
Regardless that efforts to bring about its state of existence had encountered many stochastic events, the occurrence of the state of existence of INS Mumbai was not unexpected.
For normal human existence within the local frame of reference, INS Mumbai is a non-stochastic occurrence of state, not an incident state of existence of The Delhi class. (Whereas, a time traveler across a multiverse might call the INS Mumbai an incident, or an occurrence within an incident universe.)
Whereas, for the process engineers in Palo Alto intending to produce a batch of 3GHz CPU, but received the good news from their Penang, Malaysia testing facility that 15% of those CPUs had passed 3.5GHz tests. They celebrated the good news of that incident existence of 3.5 GHz CPUs, no doubt there had merely intended to be occurrences of 3.0GHz CPUs.
The Delhi class is designed/intended to handle many types of encounters. But it is specifically intended to destroy threats with guided missiles.
Type of Encounters is the set of events The Delhi class is expected to handle. Among other members, let us presume these are some of such eventual types of encounters
- impending threats of terrestrial origin
- submarine threats
- near distance marine vessel threat
- beyond horizon marine vessel threat
- pirate vessel encounters
Let us say, that the INS Mumbai (being an occurrence of existence of The Delhi class) encountered an occurrence of the Somalian pirate vessel Dakari.
The occurrences of existence of INS Mumbai and the pirate vessel Dakari themselves were non-incident, but the encounter of the two vessels is an incident.
From the perspective of INS Mumbai, the encounter with Dakari was an instance of the event type pirate vessel encounters.
From the perspective of the Dakari, the encounter with INS Mumbai is probably an instance of which Somalian pirates might colloquially classify as event type when-outgunned-jump-overboard-and-swim-ashore.
Same incidence of an event, but classified differently by the INS Mumbai and the Dakari.
We can no doubt classify the incident of the encounter as an occurrence of an instance of {INS Mumbai->events->pirate vessel encounters}. However, being an event, especially with stochastic expectation of the event, it is more specifically an incident.