funeral director vs funeral undertaker

funeral director and funeral undertaker both are nouns.

Word	Noun	Adjective	Verb	Adverb
funeral director	Yes	No	No	No
funeral undertaker	Yes	No	No	No

As nouns, funeral director and funeral undertaker are synonyms defined as:

funeral director and funeral undertaker: one whose business is the management of funerals

Other synonyms of funeral director include mortician, undertaker.

funeral director (noun)	funeral undertaker (noun)
one whose business is the management of funerals	one whose business is the management of funerals