infinitely vs endlessly

infinitely and endlessly both are adverbs.

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

As adverbs, infinitely and endlessly are synonyms defined as:

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