incessantly vs continuously

incessantly and continuously both are adverbs.

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

As adverbs, incessantly and continuously are synonyms defined as:

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

incessantly (adverb)	continuously (adverb)
invariably	at every point
with unflagging resolve	with unflagging resolve