exordium vs introduction

exordium and introduction both are nouns.

Word	Noun	Adjective	Verb	Adverb
exordium	Yes	No	No	No
introduction	Yes	No	No	No

As nouns, introduction is a hypernym of exordium; that is, introduction is a word with a broader meaning than exordium:

exordium (noun)	introduction (noun)
(rhetoric) the introductory section of an oration or discourse	the act of putting one thing into another
	the act of beginning something new
	the act of starting something for the first time; introducing something new
	the first section of a communication
	formally making a person known to another or to the public
	a basic or elementary instructional text
	a new proposal