The spectral flux density (S) is a measure of the rate of electromagnetic-radiation-power passing through a unit area at a particular wavelength. It is commonly used in radio astronomy to characterize the power received per unit area of the antenna from an entire radio source. Thus from point sources, it is ideally consistent between antennas of different sizes. The common unit in astronomy is the jansky.
The term flux density is used similarly but over all wavelengths. It may be used specifically for all wavelengths detectable by a particular receiver or through a particular filter. Note that spectral flux density is sometimes shortened to flux density and both are sometimes shortened to flux, so paying attention to how the terms are being used is useful. For characterizing the brightness of portions of or points within a resolved (extended) source, surface brightness is typically used, which is effectively spectral flux density per region of the sky.