luxury vs self-indulgence

luxury and self-indulgence both are nouns.

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

As nouns, self-indulgence is a hypernym of luxury; that is, self-indulgence is a word with a broader meaning than luxury:

luxury: something that is an indulgence rather than a necessity
self-indulgence: an inability to resist the gratification of whims and desires

Other hypernyms of luxury include indulgence.

luxury (noun)	self-indulgence (noun)
something that is an indulgence rather than a necessity	excess in action and immoderate indulgence of bodily appetites, especially in passion or indulgence
the quality possessed by something that is excessively expensive	an inability to resist the gratification of whims and desires
wealth as evidenced by sumptuous living