pair vs occur

pair is a noun but occur is not a noun.

Word	Noun	Adjective	Verb	Adverb
pair	Yes	No	Yes	No
occur	No	No	Yes	No

As verbs, occur is a hypernym of pair; that is, occur is a word with a broader meaning than pair:

pair (noun)	occur (noun)
two people considered as a unit
a set of two similar things considered as a unit
a poker hand with 2 cards of the same value
two items of the same kind

pair (verb)	occur (verb)
engage in sexual intercourse	come to pass
bring two objects, ideas, or people together	come to one's mind; suggest itself
arrange in pairs	to be found to exist
occur in pairs
form a pair or pairs