exception vs omission

exception and omission both are nouns.

Word	Noun	Adjective	Verb	Adverb
exception	Yes	No	No	No
omission	Yes	No	No	No

As nouns, omission is a hypernym of exception; that is, omission is a word with a broader meaning than exception:

exception (noun)	omission (noun)
a deliberate act of omission	a mistake resulting from neglect
an instance that does not conform to a rule or generalization	neglecting to do something; leaving out or passing over something
grounds for adverse criticism	any process whereby sounds or words are left out of spoken words or phrases
	something that has been omitted