gradually vs step by step

gradually and step by step both are adverbs.

Word	Noun	Adjective	Verb	Adverb
gradually	No	No	No	Yes
step by step	No	No	No	Yes

As adverbs, gradually and step by step are synonyms defined as:

Other synonyms of gradually include bit by bit.

gradually (adverb)	step by step (adverb)
in a gradual manner	in a gradual manner
	proceeding in steps