inmate vs patient

inmate and patient both are nouns.

Word	Noun	Adjective	Verb	Adverb
inmate	Yes	No	No	No
patient	Yes	Yes	No	No

As nouns, patient is a hypernym of inmate; that is, patient is a word with a broader meaning than inmate:

inmate (noun)	patient (noun)
one of several resident of a dwelling (especially someone confined to a prison or hospital)	the semantic role of an entity that is not the agent but is directly involved in or affected by the happening denoted by the verb in the clause
a patient who is residing in the hospital where he is being treated	a person who requires medical care
a person serving a sentence in a jail or prison

inmate (adjective)	patient (adjective)
	enduring trying circumstances with even temper or characterized by such endurance