future vs by-and-by

future and by-and-by both are nouns.

Word	Noun	Adjective	Verb	Adverb
future	Yes	Yes	No	No
by-and-by	Yes	No	No	No

As nouns, by-and-by is a hyponym of future; that is, by-and-by is a word with a more specific, narrower meaning than future:

Other hyponyms of future include kingdom come, offing, tomorrow, manana.

future (noun)	by-and-by (noun)
bulk commodities bought or sold at an agreed price for delivery at a specified future date	an indefinite time in the future
a verb tense that expresses actions or states in the future
the time yet to come

future (adjective)	by-and-by (adjective)
yet to be or coming
a verb tense or other formation referring to events or states that have not yet happened
(of elected officers) elected but not yet serving
effective in or looking toward the future