omission vs failure

omission and failure both are nouns.

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

As nouns, failure is a hyponym of omission; that is, failure is a word with a more specific, narrower meaning than omission:

omission (noun)	failure (noun)
a mistake resulting from neglect	an act that fails
neglecting to do something; leaving out or passing over something	an unexpected omission
any process whereby sounds or words are left out of spoken words or phrases	an event that does not accomplish its intended purpose
something that has been omitted	a person with a record of failing; someone who loses consistently
	lack of success
	loss of ability to function normally
	inability to discharge all your debts as they come due