hurt vs anguish

hurt and anguish both are nouns.

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

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

Other hyponyms of hurt include torment, torture, self-torment, self-torture, tsoris, wound.

As verbs, hurt and anguish are synonyms defined as:

Other synonyms of hurt include pain.

hurt (noun)	anguish (noun)
the act of damaging something or someone	extreme mental distress
a damage or loss	extreme distress of body or mind
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

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

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