initiation vs inaugural

initiation and inaugural both are nouns.

Word	Noun	Adjective	Verb	Adverb
initiation	Yes	No	No	No
inaugural	Yes	Yes	No	No

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

initiation (noun)	inaugural (noun)
the act of starting something for the first time; introducing something new	the ceremonial induction into a position
an act that sets in motion some course of events	an address delivered at an inaugural ceremony (especially by a United States president)
wisdom as evidenced by the possession of knowledge
a formal entry into an organization or position or office

initiation (adjective)	inaugural (adjective)
	occurring at or characteristic of a formal investiture or induction
	serving to set in motion