The goal of the present paper is to better understand the mechanisms of light scattering from randomly rough surfaces,both dielectric and metal surfaces. We compare two vector scattering theories that are commonly used and that are simple to imoolement. The two theories are a first-order perturbation theory by J.M. Elson and an asymptotic theory by D. Maystre et al. We work in one dimension and compare the two theories with each other for surfaces having different values of the root-mean-square (rms) roughness and of the lateral correlation length σ. The surface profiles used are those of various real surfaces measured with a Talystep profilometer. In order to relate the numerical results to experimental data we compare them with measurements of the total integrated scattering (TIS) and with calculations of TIS.