annoyance vs seeing red

annoyance and seeing red both are nouns.

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

As nouns, seeing red is a hyponym of annoyance; that is, seeing red is a word with a more specific, narrower meaning than annoyance:

Other hyponyms of annoyance include bummer, huff, miff, pinprick, impatience, restlessness, snit.

annoyance (noun)	seeing red (noun)
the act of troubling or annoying someone	a state of irritation or annoyance
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