endlessly vs infinitely

endlessly and infinitely both are adverbs.

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

As adverbs, endlessly and infinitely are synonyms defined as:

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