unwritten vs ad-lib

unwritten is not a noun while ad-lib is a noun.

Word	Noun	Adjective	Verb	Adverb
unwritten	No	Yes	No	No
ad-lib	Yes	Yes	Yes	No

As adjectives, unwritten and ad-lib are synonyms defined as:

unwritten and ad-lib: said or done without having been planned or written in advance

Other synonyms of unwritten include spontaneous.

unwritten (noun)	ad-lib (noun)
	remark made spontaneously without prior preparation

unwritten (adjective)	ad-lib (adjective)
based on custom rather than documentation	with little or no preparation or forethought
using speech rather than writing	said or done without having been planned or written in advance
said or done without having been planned or written in advance

unwritten (verb)	ad-lib (verb)
	perform without preparation