aphaeresis vs omission

aphaeresis and omission both are nouns.

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

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

aphaeresis: (linguistics) omission at the beginning of a word as in `coon' for `raccoon' or `till' for `until'
omission: any process whereby sounds or words are left out of spoken words or phrases

Other hypernyms of aphaeresis include deletion.

aphaeresis (noun)	omission (noun)
(linguistics) omission at the beginning of a word as in `coon' for `raccoon' or `till' for `until'	a mistake resulting from neglect
	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