detergent vs cleaner

detergent and cleaner both are nouns.

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

As nouns, cleaner is a hypernym of detergent; that is, cleaner 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
cleaner: a preparation used in cleaning something

Other hypernyms of detergent include cleanser, cleansing agent.

detergent (noun)	cleaner (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	someone whose occupation is cleaning
	the operator of dry-cleaning establishment

detergent (adjective)	cleaner (adjective)
having cleansing power