local post office vs branch

local post office and branch both are nouns.

Word	Noun	Adjective	Verb	Adverb
local post office	Yes	No	No	No
branch	Yes	No	Yes	No

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

Other hypernyms of local post office include arm, subdivision.

local post office (noun)	branch (noun)
a local branch where postal services are available	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

local post office (verb)	branch (verb)
	divide into two or more branches so as to form a fork
	grow and send out branches or branch-like structures