however vs at the same time

however and at the same time both are adverbs.

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

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

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

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

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