past vs bygone

past and bygone both are nouns.

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

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

past (noun)	bygone (noun)
a verb tense that expresses actions or states in the past	past events to be put aside
the time that has elapsed
a earlier period in someone's life (especially one that they have reason to keep secret)

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earlier than the present time; no longer current	well in the past; former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

past (adverb)	bygone (adverb)
so as to pass a given point