brain damage vs harm

brain damage and harm both are nouns.

Word	Noun	Adjective	Verb	Adverb
brain damage	Yes	No	No	No
harm	Yes	No	Yes	No

As nouns, harm is a hypernym of brain damage; that is, harm is a word with a broader meaning than brain damage:

brain damage: injury to the brain that impairs its functions (especially permanently); can be caused by trauma to the head, infection, hemorrhage, inadequate oxygen, genetic abnormality, etc.
harm: any physical damage to the body caused by violence or accident or fracture etc.; the condition of an injury

Other hypernyms of brain damage include nervous disorder, neurological disease, neurological disorder, hurt, injury, trauma.

brain damage (noun)	harm (noun)
injury to the brain that impairs its functions (especially permanently); can be caused by trauma to the head, infection, hemorrhage, inadequate oxygen, genetic abnormality, etc.	the act of damaging something or someone
	the occurrence of a change for the worse
	any physical damage to the body caused by violence or accident or fracture etc.; the condition of an injury

brain damage (verb)	harm (verb)
	cause or do harm to