dentifrice vs cleaner

dentifrice and cleaner both are nouns.

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

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

Other hypernyms of dentifrice include cleanser, cleansing agent.

dentifrice (noun)	cleaner (noun)
a substance for cleaning the teeth; applied with a toothbrush	a preparation used in cleaning something
	someone whose occupation is cleaning
	the operator of dry-cleaning establishment