ad libitum vs ad lib

ad libitum and ad lib both are adverbs.

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

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

Other synonyms of ad libitum include impromptu, spontaneously.

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