at the same time vs nevertheless

at the same time and nevertheless both are adverbs.

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

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

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

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

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