deadly sin vs luxuria

deadly sin and luxuria both are nouns.

Word	Noun	Adjective	Verb	Adverb
deadly sin	Yes	No	No	No
luxuria	Yes	No	No	No

As nouns, luxuria is a hyponym of deadly sin; that is, luxuria is a word with a more specific, narrower meaning than deadly sin:

deadly sin: an unpardonable sin entailing a total loss of grace
luxuria: self-indulgent sexual desire (personified as one of the deadly sins)

deadly sin (noun)	luxuria (noun)
an unpardonable sin entailing a total loss of grace	self-indulgent sexual desire (personified as one of the deadly sins)