ad lib vs ad libitum

ad lib and ad libitum both are adverbs.

Word	Noun	Adjective	Verb	Adverb
ad lib	No	No	No	Yes
ad libitum	No	No	No	Yes

As adverbs, ad lib and ad libitum are synonyms defined as:

Other synonyms of ad lib include impromptu, spontaneously.

ad lib (adverb)	ad libitum (adverb)
without advance preparation	without advance preparation