half-brother vs blood brother

half-brother and blood brother both are nouns.

Word	Noun	Adjective	Verb	Adverb
half-brother	Yes	No	No	No
blood brother	Yes	No	No	No

As nouns, blood brother is a hypernym of half-brother; that is, blood brother is a word with a broader meaning than half-brother:

Other hypernyms of half-brother include brother.

half-brother (noun)	blood brother (noun)
a brother who has only one parent in common with you	a male with the same parents as someone else
	a male sworn (usually by a ceremony involving the mingling of blood) to treat another as his brother