tree branch vs bough

tree branch and bough both are nouns.

Word	Noun	Adjective	Verb	Adverb
tree branch	Yes	No	No	No
bough	Yes	No	No	No

As nouns, bough is a hyponym of tree branch; that is, bough is a word with a more specific, narrower meaning than tree branch:

tree branch: any of the main branches arising from the trunk or a bough of a tree
bough: any of the larger branches of a tree

Other hyponyms of tree branch include stick.

tree branch (noun)	bough (noun)
any of the main branches arising from the trunk or a bough of a tree	any of the larger branches of a tree