bilateralism vs symmetry

bilateralism and symmetry both are nouns.

Word	Noun	Adjective	Verb	Adverb
bilateralism	Yes	No	No	No
symmetry	Yes	No	No	No

As nouns, symmetry is a hypernym of bilateralism; that is, symmetry is a word with a broader meaning than bilateralism:

bilateralism: the property of being symmetrical about a vertical plane
symmetry: (mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane

Other hypernyms of bilateralism include balance, correspondence, symmetricalness.

bilateralism (noun)	symmetry (noun)
the property of being symmetrical about a vertical plane	(mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane
	(physics) the property of being isotropic; having the same value when measured in different directions
	balance among the parts of something