futurity vs by-and-by

futurity and by-and-by both are nouns.

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

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

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

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