argument vs last word

argument and last word both are nouns.

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

As nouns, last word is a hyponym of argument; that is, last word is a word with a more specific, narrower meaning than argument:

argument (noun)	last word (noun)
a variable in a logical or mathematical expression whose value determines the dependent variable; if f(x)=y, x is the independent variable	elegance by virtue of being fashionable
a course of reasoning aimed at demonstrating a truth or falsehood; the methodical process of logical reasoning	the final statement in a verbal argument
a discussion in which reasons are advanced for and against some proposition or proposal	an authoritative statement
a summary of the subject or plot of a literary work or play or movie
a fact or assertion offered as evidence that something is true
a contentious speech act; a dispute where there is strong disagreement
(computer science) a reference or value that is passed to a function, procedure, subroutine, command, or program