Laozi vs Lao-zi

Laozi and Lao-zi both are nouns.

Word	Noun	Adjective	Verb	Adverb
Laozi	Yes	No	No	No
Lao-zi	Yes	No	No	No

As nouns, Laozi and Lao-zi are synonyms defined as:

Laozi and Lao-zi: Chinese philosopher regarded as the founder of Taoism (6th century BC)

Other synonyms of Laozi include Lao-tse, Lao-tzu.

Laozi (noun)	Lao-zi (noun)
Chinese philosopher regarded as the founder of Taoism (6th century BC)	Chinese philosopher regarded as the founder of Taoism (6th century BC)