This is relevant to developing tools that allow comparisons of repositories, e.g. comparison of software availability (how many software packages are available; how quickly are new versions released, how current are the current versions, how many versions are released in a given time - three sides of a triangle; other comparisons might take into account stability and other criteria), such as whohas.
In any case, there are three main ways to classify repositories:
A classic example of a providence-based repository classification is given by Fedora, which is now distributed as Core and Extras. Another common classification, especially used by RPM-based distros (for no technical reason as far as I know), is "Contrib", sometimes called Community.
Arch Linux has a hybrid of these two, in that Current correspond to Core, Extra and Community are self-explanatory providence-based contrasts, but there are aso Testing and Unstable repositories, which are code-maturity classifications and mostly contain packages that would otherwise be found in Core. To make things entirely confusing, there is a repository Unsupported, to which users can contribute buildscripts, so it is actually a fourth kind of classification, which I might phrase as binary-source-buildscript. Note that distributions will provide either source or buildscripts, but not both separately.
But to return to the original big three, the most prominent example of a functional classification would be Slackware, which classifies packages into base, latex, gnome etc.; however, these are not strictly repositories in that they would be separately specified in a package manager config file. Again, many hybrids exist - in Arch Linux, we also find an underlying functional classification into "categories", which resemble those in Slackware: x11, system, network, gnome etc.
Being aware of the different classification schemes used, one can get the full benefit of tools such as whohas.