Scientific names for cats have varied ever since Swedish zoologist Karl Linnaeus, back in 1758, first named the whole cat family Felis, giving each species second and third names. Lions, for example, were Felis leo, while common cats were Felis catus.
But even Linnaeus had trouble sorting out those small cats, which do all look very much alike.
House cats were fairly easy–Felis catus domesticus. And their Old-World wild relatives, which are virtually untameable in Europe, seemed distinct, too–Felis catus ferus.
But Linnaeus also made what we would call errors today. For instance, he thought that Angoras and tortoiseshell cats were separate subspecies–F. catus angorensis and F. catus hispanicus, respectively. We know that they’re the same species with two different looks that cat fanciers sometimes combine together.
Once the taxonomy ball started rolling, more zoologists went back over the cat family. Again and again, they rearranged it into various logical groupings according to the theories of the day. After the start of the 20th century, this process was improved with insights gained from genetics.
Today, according to one of the most recent taxonomic arrangements (see this 2017 PDF for details), the cat family Felidae now has 14 genus names, not just the single Felis.
Lions are Panthera leo, and according to this source, the domestic cat is Felis catus, per Opinion 2027 of the International Commission on Zoological Nomenclature in 2003.
However, that opinion can also be taken to mean that house cats are “domestic derivatives” of the wildcat–Felis silvestris–and indeed they were wildcats until just after the last ice age, when they met us.
So you’ll see some zoologists refer to them as Felis silvestris catus in highly-cited papers like this one.
Why should laypeople care about this academic tempest in a teacup? Because its outcome might undercut every conservation law that now protects wildcats, which are endangered species.