at the same time vs however

at the same time and however both are adverbs.

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

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

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

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

at the same time (adverb)	however (adverb)
at the same instant	despite anything to the contrary (usually preceding a concession)
overlapping in duration	in whatever way or manner
despite anything to the contrary (usually preceding a concession)	to whatever degree or extent
	by contrast; on the other hand