We report a combined x-ray photon correlation spectroscopy (XPCS) and rheometry study of the evolution of concentrated suspensions of nanometer-scale colloids undergoing gelation and aging. The suspensions are comprised of silica colloids, 45 nm in diameter, coated with octadecyl-hydrocarbon chains in decalin. At high temperatures the chains form a solvated brush that stabilizes the colloids. At low temperature, the brush collapses leading to a weak, temperature-dependent, short-range attraction between the colloids that drives a reversible ergodic to nonergodic transition in the suspensions. Following a quench through this transition, the shear modulus grows exponentially with a time constant that depends strongly on temperature. XPCS measurements following such a quench characterize the evolution of the intermediate scattering function at wave vectors corresponding to interparticle length scales. The intermediate scattering function displays two features, a plateau value that provides information about constrained local dynamics in the suspensions and a terminal relaxation time that provides information about relaxation of residual stress. Both the plateau value and the terminal relaxation time increase exponentially following the quench with a time constant that closely matches the value for the growing shear modulus. Thus, a comparison between XPCS and rheometry indicates how the arrest of the particle-scale dynamics correlates with the growth in elasticity. Further, a comparison of intermediate scattering functions for suspensions with colloidal volume fractions ranging from 0.20 and 0.43 shows a qualitative variation in the temporal evolution that indicates a crossover from gel-like to glass-like dynamical arrest with increasing volume fraction.