twig vs branch

twig and branch both are nouns.

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

As nouns, branch is a hypernym of twig; that is, branch is a word with a broader meaning than twig:

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

As verbs, branch is a hypernym of twig; that is, branch is a word with a broader meaning than twig:

Other hypernyms of twig include fork, furcate, ramify, separate.

twig (noun)	branch (noun)
a small branch or division of a branch (especially a terminal division); usually applied to branches of the current or preceding year	any projection that is thought to resemble a human arm
	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

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