funeral home vs mortuary

funeral home and mortuary both are nouns.

Word	Noun	Adjective	Verb	Adverb
funeral home	Yes	No	No	No
mortuary	Yes	Yes	No	No

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

funeral home: a mortuary where those who knew the deceased can come to pay their last respects
mortuary: a building (or room) where dead bodies are kept before burial or cremation

Other hypernyms of funeral home include dead room, morgue.

funeral home (noun)	mortuary (noun)
a mortuary where those who knew the deceased can come to pay their last respects	a building (or room) where dead bodies are kept before burial or cremation

funeral home (adjective)	mortuary (adjective)
	of or relating to a funeral
	of or relating to or characteristic of death