The word cat is the same in a lot of languages, for the same reason that Coca-Cola is the same in even more languages. Because most cats were domesticated, and originated, in one place: Egypt.
Not all cats: there was a separate domestication, Wikipedia tells me (Cat), in China. And extremely early domestication in Cyprus as well. (It’s one of those cruel ironies of fate that the site for the 7500 BC cat find in Cyprus is Shillourokambos. “Dog Tail Plain.”)
But the main site from which the languages you have in mind got their word—and their speakers got their cats—was Egypt: we think it’s from the Late Egyptian (1300–700 BC) čaute, ‘female wildcat’. That gave us, inter alia,
- Latin cattus, and all its Romance, Germanic, and Slavonic progeny. Which includes Byzantine Greek kata, from cattus, and Modern Greek ɣata, from Italian gatto .
- Egyptian Arabic keta قطة , as reported by Ahmed Ouda, and Tunisian Arabic قطّوس qaṭṭus, as reported by Wiktionary: cattus – Wiktionary
It didn’t give us Latin feles (which may be cognate with the Welsh for marten, just as the Katharevousa Greek γαλῆ is actually the ancient Greek for ferret). But at some time like 300 AD, the colloquial Roman word borrowed from Egypt started following the cat, and kept on following it throughout Europe.
I reserve especial ire in this answer for people who do not allow comments on their answers, and then write answers needing correction.