pen vs correctional institution

pen and correctional institution both are nouns.

Word	Noun	Adjective	Verb	Adverb
pen	Yes	No	Yes	No
correctional institution	Yes	No	No	No

As nouns, correctional institution is a hypernym of pen; that is, correctional institution is a word with a broader meaning than pen:

pen (noun)	correctional institution (noun)
female swan	a penal institution maintained by the government
a writing implement with a point from which ink flows
an enclosure for confining livestock
a correctional institution for those convicted of major crimes
a portable enclosure in which babies may be left to play

pen (verb)	correctional institution (verb)
produce a literary work