omission vs aphesis

omission and aphesis both are nouns.

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

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

omission: any process whereby sounds or words are left out of spoken words or phrases
aphesis: the gradual disappearance of an initial (usually unstressed) vowel or syllable as in `squire' for `esquire'

Other hyponyms of omission include aphaeresis, apheresis, elision, eclipsis, ellipsis.

omission (noun)	aphesis (noun)
a mistake resulting from neglect	the gradual disappearance of an initial (usually unstressed) vowel or syllable as in `squire' for `esquire'
neglecting to do something; leaving out or passing over something
any process whereby sounds or words are left out of spoken words or phrases
something that has been omitted