religious vs monastic

religious and monastic both are nouns.

Word	Noun	Adjective	Verb	Adverb
religious	Yes	Yes	No	No
monastic	Yes	Yes	No	No

As nouns, monastic is a hyponym of religious; that is, monastic is a word with a more specific, narrower meaning than religious:

religious: a member of a religious order who is bound by vows of poverty and chastity and obedience
monastic: a male religious living in a cloister and devoting himself to contemplation and prayer and work

Other hyponyms of religious include friar, mendicant, monk, Benedictine, Jesuit, nun, eremite, cenobite, coenobite, superior, votary.

religious (noun)	monastic (noun)
a member of a religious order who is bound by vows of poverty and chastity and obedience	a male religious living in a cloister and devoting himself to contemplation and prayer and work

religious (adjective)	monastic (adjective)
having or showing belief in and reverence for a deity	of communal life sequestered from the world under religious vows
of or relating to clergy bound by monastic vows
concerned with sacred matters or religion or the church
extremely scrupulous and conscientious