endlessly vs continuously

endlessly and continuously both are adverbs.

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

As adverbs, endlessly and continuously are synonyms defined as:

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

endlessly (adverb)	continuously (adverb)
continuing forever without end	at every point
with unflagging resolve	with unflagging resolve
all the time; seemingly without stopping
(spatial sense) seeming to have no bounds