Bear with me, I'll try to keep it basic. Starting wiith Wikipedia's definition which is about as good as anything I might come up with.
An evolutionary lineage is a temporal series of populations, organisms, cells, or genes connected by a continuous line of descent from ancestor to descendant. Lineages are typically visualized as subsets of a phylogenetic tree. A lineage is a single line of descent or linear chain within the tree, containing a single ancestor and all its descendants.
A genus is a lineage for our purposes, so it will contain the species alive today that have all descended (evolved) directly from one common ancestor. A genus like this is termed monophyletic; but a genus which includes additional species descended from another ancestor is termed polyphyletic. And the
Corydoras genus is the latter. Phylogenetic analysis of the DNA of the species is how ichthyologists sort this out.
Corydoras holds some 160 described species; described means the fish has been examined and determined to be a distinct species, for example
Corydoras paleatus. There are also dozens of discovered cories that are awaiting scientific description, and these have been assigned C or CW numbers; when they are described, they may turn out to be new distinct species, or a variant of an existing species.
What has been discovered so far is that there are nine lineages comprised of the species in
Corydoras. So the ancestor of
C. paleatus is not the same ancestor of a species in a different lineage. Species within a monophyletic genus (a lineage) may hybridize depending upon circumstances, but species from two different genera (lineages) are much less likely too, at least naturally. This has significant consequences for hobbyists keeping cories in a tank of mixed species. With the destruction of natural habitats and the extinction of species, the fish in our aquaria may become the only fish of a species (this is happening with some other fish) and while repopulation of the habitat is not usually feasible (because it has been destroyed) the species will still be with us even if it is in home or public aquaria.