indulging vs binge

indulging and binge both are nouns.

Word	Noun	Adjective	Verb	Adverb
indulging	Yes	No	No	No
binge	Yes	No	Yes	No

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

Other hyponyms of indulging include intemperance, intemperateness, self-indulgence, excess, overindulgence, orgy, splurge.

indulging (noun)	binge (noun)
the act of indulging or gratifying a desire	an occasion for excessive eating or drinking
	any act of immoderate indulgence

indulging (verb)	binge (verb)
	overeat or eat immodestly; make a pig of oneself
	to watch a large amount of media in a single seating