branch vs twig

branch and twig both are nouns.

Word	Noun	Adjective	Verb	Adverb
branch	Yes	No	Yes	No
twig	Yes	No	Yes	No

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

branch: a division of a stem, or secondary stem arising from the main stem of a plant
twig: a small branch or division of a branch (especially a terminal division); usually applied to branches of the current or preceding year

Other hyponyms of branch include deadwood, limb, tree branch, branchlet, sprig.

As verbs, twig is a hyponym of branch; that is, twig is a word with a more specific, narrower meaning than branch:

Other hyponyms of branch include arborise, arborize, bifurcate, trifurcate.

branch (noun)	twig (noun)
any projection that is thought to resemble a human arm	a small branch or division of a branch (especially a terminal division); usually applied to branches of the current or preceding year
a division of some larger or more complex organization
a stream or river connected to a larger one
a natural consequence of development
a division of a stem, or secondary stem arising from the main stem of a plant
a part of a forked or branching shape

branch (verb)	twig (verb)
divide into two or more branches so as to form a fork	branch out in a twiglike manner
grow and send out branches or branch-like structures	understand, usually after some initial difficulty