hairsbreadth vs hair's-breadth

hairsbreadth and hair's-breadth both are nouns.

Word	Noun	Adjective	Verb	Adverb
hairsbreadth	Yes	No	No	No
hair's-breadth	Yes	No	No	No

As nouns, hairsbreadth and hair's-breadth are synonyms defined as:

Other synonyms of hairsbreadth include hair, whisker.

hairsbreadth (noun)	hair's-breadth (noun)
a very small distance or space	a very small distance or space