inauguration vs commencement

inauguration and commencement both are nouns.

Word	Noun	Adjective	Verb	Adverb
inauguration	Yes	No	No	No
commencement	Yes	No	No	No

As nouns, commencement is a hypernym of inauguration; that is, commencement is a word with a broader meaning than inauguration:

Other hypernyms of inauguration include beginning, start.

inauguration (noun)	commencement (noun)
the ceremonial induction into a position	the act of starting something
the act of starting a new operation or practice	an academic exercise in which diplomas are conferred
	the time at which something is supposed to begin