annoyance vs temper

annoyance and temper both are nouns.

Word	Noun	Adjective	Verb	Adverb
annoyance	Yes	No	No	No
temper	Yes	No	Yes	No

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

Other hyponyms of annoyance include irritation, pique, frustration, aggravation, exasperation, harassment, torment, displeasure.

annoyance (noun)	temper (noun)
the act of troubling or annoying someone	the elasticity and hardness of a metal object; its ability to absorb considerable energy before cracking
something or someone that causes trouble; a source of unhappiness	a disposition to exhibit uncontrolled anger
anger produced by some annoying irritation	a characteristic (habitual or relatively temporary) state of feeling
an unpleasant person who is annoying or exasperating	a sudden outburst of anger
the psychological state of being irritated or annoyed

annoyance (verb)	temper (verb)
	make more temperate, acceptable, or suitable by adding something else
	adjust the pitch (of pianos)
	harden by reheating and cooling in oil
	change by restraining or moderating
	bring to a desired consistency, texture, or hardness by a process of gradually heating and cooling