Rabbits and cats are both mammals so somewhere back in evolutionary history they will have a common ancestor – some animal from which they both evolved. But I don’t know if a fossil of that animal has been discovered.
i suspect the name kitten is used for babies because newborn cats and rabbits may look a little similar.
If you look at foetuses of mammals, they look surprisingly similar. For example, human foetuses look similar to mouse foetuses
Rabbits and cats are related, they’re both animals, vertebrates and mammals, but they’re not particularly close cousins (as I am sure you know, a rabbit is a rodent, so closer to a rat or mouse). It doesn’t seem unreasonable to call two different fluffy baby animals by the same name, does it?