unceasingly vs continuously

unceasingly and continuously both are adverbs.

Word	Noun	Adjective	Verb	Adverb
unceasingly	No	No	No	Yes
continuously	No	No	No	Yes

As adverbs, unceasingly and continuously are synonyms defined as:

Other synonyms of unceasingly include ceaselessly, endlessly, incessantly, unendingly.

unceasingly (adverb)	continuously (adverb)
with unflagging resolve	at every point
	with unflagging resolve