The direct detection of gravitational waves has provided new opportunities for studying the Universe, but also new challenges, such as the detection and characterization of stochastic gravitational-wave backgrounds at different gravitational-wave frequencies. In this paper, we examine two different methods for their description, one based on the amplitude of a gravitational-wave signal and one on its Stokes parameters. We find that the Stokes parameters are able to describe anisotropic and correlated backgrounds, whereas the usual power spectra of the amplitudes cannot – i.e. the Stokes spectra are sensitive to properties such as the spatial distribution of the gravitational-wave sources in a realistic backgrounds.