withal vs at the same time

withal and at the same time both are adverbs.

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

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

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

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

withal (adverb)	at the same time (adverb)
together with this	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)