They are both formed when a liquid is supercooled rapidly, no free energy, and they both have irregular structures. What defines a glass other than how it is amorphous, transparent, and has a glass transition state?
While a glass is generally considered to be a supercooled, configurationally frozen liquid, not all amorphous solids are glasses. For example, amorphous silicon is a four-fold coordinated semiconducting solid, much like crystal silicon. Liquid silicon is 8-12 fold coordinated with metallic bonding. Amorphous silicon has been shown to display a first-order phase transition to both the crystal and the liquid.
So, all glasses are amorphous solids, but not all amorphous solids are glasses.