binge vs indulging

binge and indulging both are nouns.

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

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

Other hypernyms of binge include humoring, humouring, indulgence, pampering.

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

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