  We report on a comprehensive theory-simulation-experimental study of
collective and self-diffusion in suspensions of charge-stabilized colloidal
spheres. In simulation and theory, the spheres interact by a hard-core plus
screened Coulomb pair potential. Intermediate and self-intermediate scattering
functions are calculated by accelerated Stokesian Dynamics simulations where
hydrodynamic interactions (HIs) are fully accounted for. The study spans the
range from the short-time to the colloidal long-time regime. Additionally,
Brownian Dynamics simulation and mode-coupling theory (MCT) results are
generated where HIs are neglected. It is shown that HIs enhance collective and
self-diffusion at intermediate and long times, whereas at short times
self-diffusion, and for certain wavenumbers also collective diffusion, are
slowed down. MCT significantly overestimate the slowing influence of dynamic
particle caging. The simulated scattering functions are in decent agreement
with our dynamic light scattering (DLS) results for suspensions of charged
silica spheres. Simulation and theoretical results are indicative of a
long-time exponential decay of the intermediate scattering function. The
approximate validity of a far-reaching time-wavenumber factorization of the
scattering function is shown to be a consequence of HIs. Our study of
collective diffusion is amended by simulation and theoretical results for the
self-intermediate scattering function and the particle mean squared
displacement (MSD). Since self-diffusion is not assessed in DLS measurements, a
method to deduce the MSD approximately in DLS is theoretically validated.
