symmetry vs equilibrium

symmetry and equilibrium both are nouns.

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

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

Other hypernyms of symmetry include balance, counterbalance, equipoise.

symmetry (noun)	equilibrium (noun)
(mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane	a sensory system located in structures of the inner ear that registers the orientation of the head
(physics) the property of being isotropic; having the same value when measured in different directions	a chemical reaction and its reverse proceed at equal rates
balance among the parts of something	equality of distribution
	a stable situation in which forces cancel one another