Molecular dynamics simulations of the temperature dependent crystal growth rates of the salts, NaCl and ZnS, from their melts are reported, along with those of a number of pure metals. The growth rate of NaCl and the FCC-forming metals show little evidence of activated control, while that of ZnS and Fe, a BCC forming metal, exhibit activation barriers similar to those observed for diffusion in the melt. Unlike ZnS and Fe, the interfacial inherent structures of NaCl and Cu and Ag are found to be crystalline. We calculate the median displacement between the interfacial liquid and crystalline states and show that this distance is smaller than the cage length, demonstrating that crystal growth in the fast crystallizers can occur via local vibrations and so largely avoid the activated kinetics associated with the larger displacements associated with particle transport.