cleansing milk vs cleaner

cleansing milk and cleaner both are nouns.

Word	Noun	Adjective	Verb	Adverb
cleansing milk	Yes	No	No	No
cleaner	Yes	No	No	No

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

cleansing milk: A face cleanser that is similar in texture to condensed milk.
cleaner: a preparation used in cleaning something

Other hypernyms of cleansing milk include cleanser, cleansing agent.

cleansing milk (noun)	cleaner (noun)
A face cleanser that is similar in texture to condensed milk.	a preparation used in cleaning something
	someone whose occupation is cleaning
	the operator of dry-cleaning establishment