by-and-by vs hereafter

by-and-by and hereafter both are nouns.

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

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

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

by-and-by (noun)	hereafter (noun)
an indefinite time in the future	the time yet to come
	life after death

by-and-by (adverb)	hereafter (adverb)
	in a subsequent part of this document or statement or matter etc.
	following this in time or order or place; after this
	in a future life or state