They are different species, in conventional Linnaean classification, within the cat kind.
Why stop there?
Cats, dogs, seals, and bears (to name a few) are part of the Carnivora kind. We are also part of the mammal kind with other mammal species. There is also the amniote, vertebrate, and eukaryote kinds.
Of course that then raises an issue with the Biological Species concept which says a species consists of populations of organisms that can reproduce with one another and that are reproductively isolated from other populations. That would mean that if you can get a fertile hybrid then they would be part of the same species. This is part of what is known as the Species Problem.
The Species Problem is a human problem. There is no law in nature that says species must fit into black and white categories because humans want them to. The Species Problem is simply human bias.
If evolution is true then we should have the "Species Problem". Complete speciation doesn't occur in a single generation with evolution, so there should be a period of time where separate populations should still be able to produce fertile offspring.
Hybridisation chains then provide one objective criteria for mapping which species belong to which kind. However it is also possible for species within the one kind to be fully reproductively isolated.
The second sentence contradicts the first sentence.
If the links in that chain of hybridization are lost to extinction then you would have two separate kinds as determined by hybridization.
Added in edit:
I would also be curious to an answer to this question. Would you consider the genetic differences between species in the "cat kind" to be a good measure for what constitutes a kind?
You couldn't call it a Family since some Families in the current Linnaean system could contain more than one Kind.
Given your inability to define what a kind is, how could you know which species belong to which kinds?
Edited by Taq, : No reason given.