laterality vs asymmetry

laterality and asymmetry both are nouns.

Word	Noun	Adjective	Verb	Adverb
laterality	Yes	No	No	No
asymmetry	Yes	No	No	No

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

laterality (noun)	asymmetry (noun)
superior development of one side of the body	(mathematics) a lack of symmetry
the property of using one hand more than the other
localization of function on either the right or left sides of the brain