by-and-by vs future

by-and-by and future both are nouns.

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

As nouns, future is a hypernym of by-and-by; that is, future is a word with a broader meaning than by-and-by:

Other hypernyms of by-and-by include futurity, hereafter, time to come.

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

by-and-by (adjective)	future (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