We present a comprehensive account of the dynamics of layer-displacement fluctuations in smectic liquid-crystal membranes as studied by x-ray photon correlation spectroscopy (XPCS) and neutron-spin echo (NSE). Combining these two techniques at fast relaxation times, three distinct relaxation regimes can be distinguished. For thin membranes, at the specular Bragg position oscillatory relaxation occurs, which transforms for thicker samples into exponential decay. Above a critical off-specular angle, in XPCS exponential relaxation is observed that does not depend on the scattering angle. This indicates relaxation times that are independent of the wavelength of the fluctuations. In this regime the relaxation of the fluctuations is dominated by the surface tension. Using NSE larger off-specular angles can be reached than by XPCS, for which the relaxation time decreases with the scattering angle. This regime is dominated by the bulk elasticity of the smectic membrane. The results are compared with theoretical models for the fluctuation behavior of smectic membranes, in which effects of the mosaic distribution and of the center of mass movement of the smectic membranes must be incorporated.