The Stefan-Boltzmann law describes blackbody radiation in terms of radiant flux per unit area i.e. how much energy passes through a 2D surface per unit time. I find this very simple and I understand how to do calculations with it.
Planck's law describes blackbody radiation (per frequency) either as volumetric energy density (which volume?) or as radiance which seems to have the units of flux per unit area per steradian. This supposedly makes the unit invariant over distance, but I haven't been able to wrap my head around what it's actually describing or how to do calculations with it.
How do I convert the values of Planck's law into the same units as Stefan-Boltzmann's law? Once I have that I know how to find the total radiative power of the object by multiplying by its surface area, and I find that a very concrete quantity to think about.