mortician vs undertaker

mortician and undertaker both are nouns.

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

As nouns, mortician and undertaker are synonyms defined as:

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

Other synonyms of mortician include funeral director, funeral undertaker.

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