home help vs domestic help

home help and domestic help both are nouns.

Word	Noun	Adjective	Verb	Adverb
home help	Yes	No	No	No
domestic help	Yes	No	No	No

As nouns, domestic help is a hypernym of home help; that is, domestic help is a word with a broader meaning than home help:

home help: a person hired to help in another's home (especially one employed by a local authority to help the infirm with domestic work)
domestic help: a servant who is paid to perform menial tasks around the household

Other hypernyms of home help include domestic, house servant.

home help (noun)	domestic help (noun)
a person hired to help in another's home (especially one employed by a local authority to help the infirm with domestic work)	a servant who is paid to perform menial tasks around the household