seeing red vs annoyance

seeing red and annoyance both are nouns.

Word	Noun	Adjective	Verb	Adverb
seeing red	Yes	No	No	No
annoyance	Yes	No	No	No

As nouns, annoyance is a hypernym of seeing red; that is, annoyance is a word with a broader meaning than seeing red:

Other hypernyms of seeing red include botheration, irritation, vexation.

seeing red (noun)	annoyance (noun)
a state of irritation or annoyance	the act of troubling or annoying someone
	something or someone that causes trouble; a source of unhappiness
	anger produced by some annoying irritation
	an unpleasant person who is annoying or exasperating
	the psychological state of being irritated or annoyed