There are two possible approaches to describe a population of astrophysical gravitational wave (GW) sources: one can focus on high signal-to-noise sources that can be detected individually, and build a catalogue. Alternatively, one can take a background-approach and study the incoherent superposition of all GW signals emitted by the entire population, from the onset of stellar activity until today.  A detailed description of signals from resolvable events, and of the properties of a stochastic background, including propagation effects, is crucial to extract accurate information on the underlying source population.  Moreover, once combined, these two observables can provide insight on the properties of a faint and distant sub-population that cannot be accessed with any other means of observation. In my talk, I will outline the differences and the complementarity of these two descriptions, from the point of view of observations and of theoretical modeling, and stress a few caveats to be kept in mind when deriving predictions to be compared with (present and future) datasets.