lang syne vs old times

lang syne and old times both are nouns.

Word	Noun	Adjective	Verb	Adverb
lang syne	Yes	No	No	Yes
old times	Yes	No	No	No

As nouns, lang syne and old times are synonyms defined as:

Other synonyms of lang syne include auld langsyne, good old days, langsyne.

lang syne (noun)	old times (noun)
past times remembered with nostalgia	past times remembered with nostalgia

lang syne (adverb)	old times (adverb)
of the distant or comparatively distant past