cleaning woman vs cleaner

cleaning woman and cleaner both are nouns.

Word	Noun	Adjective	Verb	Adverb
cleaning woman	Yes	No	No	No
cleaner	Yes	No	No	No

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

Other hypernyms of cleaning woman include adult female, woman.

cleaning woman (noun)	cleaner (noun)
a human female employed to do housework	a preparation used in cleaning something
	someone whose occupation is cleaning
	the operator of dry-cleaning establishment