past vs yesterday

past and yesterday both are nouns.

Word	Noun	Adjective	Verb	Adverb
past	Yes	Yes	No	Yes
yesterday	Yes	No	No	Yes

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

past (noun)	yesterday (noun)
a verb tense that expresses actions or states in the past	the recent past
the time that has elapsed	the day immediately before today
a earlier period in someone's life (especially one that they have reason to keep secret)

past (adjective)	yesterday (adjective)
earlier than the present time; no longer current
of a person who has held and relinquished a position or office

past (adverb)	yesterday (adverb)
so as to pass a given point	on the day preceding today
	in the recent past; only a short time ago