mortician vs funeral undertaker

mortician and funeral undertaker both are nouns.

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

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

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

Other synonyms of mortician include funeral director, undertaker.

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