last word vs authority

last word and authority both are nouns.

Word	Noun	Adjective	Verb	Adverb
last word	Yes	No	No	No
authority	Yes	No	No	No

As nouns, authority is a hypernym of last word; that is, authority is a word with a broader meaning than last word:

last word (noun)	authority (noun)
elegance by virtue of being fashionable	the power or right to give orders or make decisions
the final statement in a verbal argument	official permission or approval
an authoritative statement	freedom from doubt; belief in yourself and your abilities
	an authoritative written work
	an administrative unit of government
	an expert whose views are taken as definitive
	(usually plural) persons who exercise (administrative) control over others