bit by bit vs in stages

bit by bit and in stages both are adverbs.

Word	Noun	Adjective	Verb	Adverb
bit by bit	No	No	No	Yes
in stages	No	No	No	Yes

As adverbs, bit by bit and in stages are synonyms defined as:

Other synonyms of bit by bit include little by little, piecemeal.

bit by bit (adverb)	in stages (adverb)
in a gradual manner	a little bit at a time
a little bit at a time