creme cleanser vs cleaner

creme cleanser and cleaner both are nouns.

Word	Noun	Adjective	Verb	Adverb
creme cleanser	Yes	No	No	No
cleaner	Yes	No	No	No

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

creme cleanser: A skin cleanser that comes in a thick liquid form, similar in texture to a lotion.
cleaner: a preparation used in cleaning something

Other hypernyms of creme cleanser include cleanser, cleansing agent, cosmetic.

creme cleanser (noun)	cleaner (noun)
A skin cleanser that comes in a thick liquid form, similar in texture to a lotion.	a preparation used in cleaning something
	someone whose occupation is cleaning
	the operator of dry-cleaning establishment