indulging vs indulgence

indulging and indulgence both are nouns.

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

As nouns, indulging and indulgence are synonyms defined as:

Other synonyms of indulging include humoring, humouring, pampering.

indulging (noun)	indulgence (noun)
the act of indulging or gratifying a desire	the act of indulging or gratifying a desire
	foolish or senseless behavior
	the remission by the pope of the temporal punishment in purgatory that is still due for sins even after absolution
	an inability to resist the gratification of whims and desires
	a disposition to yield to the wishes of someone