purging vs cleansing

purging and cleansing both are nouns.

Word	Noun	Adjective	Verb	Adverb
purging	Yes	Yes	No	No
cleansing	Yes	Yes	No	No

As nouns, cleansing is a hypernym of purging; that is, cleansing is a word with a broader meaning than purging:

purging: an act of removing by cleansing; ridding of sediment or other undesired elements
cleansing: the act of making something clean

Other hypernyms of purging include cleaning, cleanup.

purging (noun)	cleansing (noun)
an act of removing by cleansing; ridding of sediment or other undesired elements	the act of making something clean
the act of clearing yourself (or another) from some stigma or charge

purging (adjective)	cleansing (adjective)
serving to purge or rid of sin	acting like an antiseptic
	cleansing the body by washing; especially ritual washing of e.g. hands