self-indulgence vs indulging

self-indulgence and indulging both are nouns.

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

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

self-indulgence: excess in action and immoderate indulgence of bodily appetites, especially in passion or indulgence
indulging: the act of indulging or gratifying a desire

Other hypernyms of self-indulgence include humoring, humouring, indulgence, pampering.

self-indulgence (noun)	indulging (noun)
excess in action and immoderate indulgence of bodily appetites, especially in passion or indulgence	the act of indulging or gratifying a desire
an inability to resist the gratification of whims and desires