brother vs half-brother

brother and half-brother both are nouns.

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

As nouns, half-brother is a hyponym of brother; that is, half-brother is a word with a more specific, narrower meaning than brother:

Other hyponyms of brother include big brother, little brother, half brother, stepbrother.

brother (noun)	half-brother (noun)
a male with the same parents as someone else	a brother who has only one parent in common with you
a male person who is a fellow member (of a fraternity or religion or other group)
a close friend who accompanies his buddies in their activities
used as a term of address for those male persons engaged in the same movement