pain vs mental anguish

pain and mental anguish both are nouns.

Word	Noun	Adjective	Verb	Adverb
pain	Yes	No	Yes	No
mental anguish	Yes	No	No	No

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

Other hyponyms of pain include growing pains, unpleasantness, hurt, suffering, distress, hurt, suffering.

pain (noun)	mental anguish (noun)
a somatic sensation of acute discomfort	sustained dull painful emotion
something or someone that causes trouble; a source of unhappiness
emotional distress; a fundamental feeling that people try to avoid
a symptom of some physical hurt or disorder

pain (verb)	mental anguish (verb)
cause bodily suffering to and make sick or indisposed
cause emotional anguish or make miserable