up to now vs as yet

up to now and as yet both are adverbs.

Word	Noun	Adjective	Verb	Adverb
up to now	No	No	No	Yes
as yet	No	No	No	Yes

As adverbs, up to now and as yet are synonyms defined as:

up to now and as yet: used in negative statement to describe a situation that has existed up to this point or up to the present time

Other synonyms of up to now include heretofore, hitherto, so far, thus far, til now, until now, yet.

up to now (adverb)	as yet (adverb)
used in negative statement to describe a situation that has existed up to this point or up to the present time	used in negative statement to describe a situation that has existed up to this point or up to the present time
prior to the present time