corrections vs local department

corrections and local department both are nouns.

Word	Noun	Adjective	Verb	Adverb
corrections	Yes	No	No	No
local department	Yes	No	No	No

As nouns, local department is a hypernym of corrections; that is, local department is a word with a broader meaning than corrections:

corrections: the department of local government that is responsible for managing the treatment of convicted offenders
local department: a permanent department created to perform the work of a local government

Other hypernyms of corrections include department of local government.

corrections (noun)	local department (noun)
the social control of offenders through a system of imprisonment and rehabilitation and probation and parole	a permanent department created to perform the work of a local government
the department of local government that is responsible for managing the treatment of convicted offenders