left-handedness vs laterality

left-handedness and laterality both are nouns.

Word	Noun	Adjective	Verb	Adverb
left-handedness	Yes	No	No	No
laterality	Yes	No	No	No

As nouns, laterality is a hypernym of left-handedness; that is, laterality is a word with a broader meaning than left-handedness:

Other hypernyms of left-handedness include handedness.

left-handedness (noun)	laterality (noun)
preference for using the left hand	superior development of one side of the body
the status of being born of a morganatic marriage	the property of using one hand more than the other
	localization of function on either the right or left sides of the brain