past vs old times

past and old times both are nouns.

Word	Noun	Adjective	Verb	Adverb
past	Yes	Yes	No	Yes
old times	Yes	No	No	No

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

past (noun)	old times (noun)
a verb tense that expresses actions or states in the past	past times remembered with nostalgia
the time that has elapsed
a earlier period in someone's life (especially one that they have reason to keep secret)

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earlier than the present time; no longer current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

past (adverb)	old times (adverb)
so as to pass a given point