A consensus is emerging that discontinuous shear thickening (DST) in dense suspensions marks a transition from a flow state where particles remain well separated by lubrication layers, to one dominated by frictional contacts. We show here that reasonable assumptions about contact proliferation predict two distinct types of DST in the absence of inertia. The first occurs at densities above the jamming point of frictional particles; here, the thickened state is completely jammed and (unless particles deform) cannot flow without inhomogeneity or fracture. The second regime shows strain-rate hysteresis and arises at somewhat lower densities, where the thickened phase flows smoothly. DST is predicted to arise when finite-range repulsions defer contact formation until a characteristic stress level is exceeded. © 2014 American Physical Society.