all the same vs at the same time

all the same and at the same time both are adverbs.

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

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

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

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

all the same (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)