  Glasses and gels are the two dynamically arrested, disordered states of
matter. Despite their importance, their similarities and differences remain
elusive, especially at high density. We identify dynamical and structural
signatures which distinguish the gel and glass transitions in a colloidal model
system of hard and "sticky" spheres. Gelation is induced by crossing the
gas-liquid phase-separation line and the resulting rapid densification of the
colloid-rich phase leads to a sharp change in dynamics and local structure.
Thus, we find that gelation is first-order-like and can occur at much higher
densities than previously thought: far from being low-density networks, gels
have a clear "thermodynamic" definition which nevertheless leads to a
non-equilibrium state with a distinct local structure characteristic of a
rapidly quenched glass. In contrast, approaching the glass transition, the
dynamics slow continuously accompanied by the emergence of local five-fold
symmetric structure. Our findings provide a general thermodynamic, kinetic, and
structural basis upon which to distinguish gelation from vitrification.
