nevertheless vs at the same time

nevertheless and at the same time both are adverbs.

Word	Noun	Adjective	Verb	Adverb
nevertheless	No	No	No	Yes
at the same time	No	No	No	Yes

As adverbs, nevertheless and at the same time are synonyms defined as:

nevertheless and at the same time: despite anything to the contrary (usually preceding a concession)

Other synonyms of nevertheless include all the same, even so, however, nonetheless, notwithstanding, still, withal, yet.

nevertheless (adverb)	at the same time (adverb)
despite anything to the contrary (usually preceding a concession)	at the same instant
	overlapping in duration
	despite anything to the contrary (usually preceding a concession)