by-and-by vs futurity

by-and-by and futurity both are nouns.

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

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

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

by-and-by (noun)	futurity (noun)
an indefinite time in the future	the quality of being in or of the future
	the time yet to come