indulgence vs luxury

indulgence and luxury both are nouns.

Word	Noun	Adjective	Verb	Adverb
indulgence	Yes	No	No	No
luxury	Yes	No	No	No

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

indulgence (noun)	luxury (noun)
the act of indulging or gratifying a desire	something that is an indulgence rather than a necessity
foolish or senseless behavior	the quality possessed by something that is excessively expensive
the remission by the pope of the temporal punishment in purgatory that is still due for sins even after absolution	wealth as evidenced by sumptuous living
an inability to resist the gratification of whims and desires
a disposition to yield to the wishes of someone