co-occurrence vs natural event

co-occurrence and natural event both are nouns.

Word	Noun	Adjective	Verb	Adverb
co-occurrence	Yes	No	No	No
natural event	Yes	No	No	No

As nouns, natural event is a hypernym of co-occurrence; that is, natural event is a word with a broader meaning than co-occurrence:

co-occurrence: an event or situation that happens at the same time as or in connection with another
natural event: an event that happens

Other hypernyms of co-occurrence include happening, occurrence, occurrent.

co-occurrence (noun)	natural event (noun)
the temporal property of two things happening at the same time	an event that happens
an event or situation that happens at the same time as or in connection with another