Generally, most SPAAG's are reloaded from trucks. While they have prestigious rates of fire from their guns, they tend to fire in short bursts. Few if any of them would be able to fire their sustained rate of fire without melting the barrels. A few have reloading "cassettes" which allow their ammunition supply to be reloaded in one, quick hit. However, that generally requires rear access and large hatches. As most SPAAG are conversions from other vehicles, they often have to be reloaded through small ammunition hatches on the turret/hull top.
Most SAMs have specialised reloading vehicles - usually truck mounted, equipped with cranes to handle the large, heavy usually awkwardly shaped missiles. The Soviets were very good with that, having specialised vehicles in first, second and third line which were designed to speedily allow the reloading on the launchers and their supply vehicles.