detergent vs cleanser

detergent and cleanser both are nouns.

Word	Noun	Adjective	Verb	Adverb
detergent	Yes	Yes	No	No
cleanser	Yes	No	No	No

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

detergent: a cleansing agent that differs from soap but can also emulsify oils and hold dirt in suspension
cleanser: a preparation used in cleaning something

Other hypernyms of detergent include cleaner, cleansing agent.

detergent (noun)	cleanser (noun)
a cleansing agent that differs from soap but can also emulsify oils and hold dirt in suspension	a preparation used in cleaning something
a surface-active chemical widely used in industry and laundering

detergent (adjective)	cleanser (adjective)
having cleansing power