by the way vs incidentally

by the way and incidentally both are adverbs.

Word	Noun	Adjective	Verb	Adverb
by the way	No	No	No	Yes
incidentally	No	No	No	Yes

As adverbs, by the way and incidentally are synonyms defined as:

Other synonyms of by the way include apropos, by the bye.

by the way (adverb)	incidentally (adverb)
introducing a different topic	introducing a different topic
	of a minor or subordinate nature