anguish vs hurt

anguish and hurt both are nouns.

Word	Noun	Adjective	Verb	Adverb
anguish	Yes	No	Yes	No
hurt	Yes	Yes	Yes	No

As nouns, hurt is a hypernym of anguish; that is, hurt is a word with a broader meaning than anguish:

Other hypernyms of anguish include distress, suffering.

As verbs, anguish and hurt are synonyms defined as:

Other synonyms of anguish include pain.

anguish (noun)	hurt (noun)
extreme mental distress	the act of damaging something or someone
extreme distress of body or mind	a damage or loss
	feelings of mental or physical pain
	psychological suffering
	any physical damage to the body caused by violence or accident or fracture etc.; the condition of an injury

anguish (adjective)	hurt (adjective)
	damaged; used of inanimate objects or their value
	suffering from physical injury especially that suffered in battle

anguish (verb)	hurt (verb)
cause emotional anguish or make miserable	give trouble or pain to
suffer great pains or distress	be in pain
	cause damage or affect negatively
	hurt the feelings of
	cause emotional anguish or make miserable
	be the source of pain
	feel physical pain