Nowadays it’s called the Permesso di Soggiorno EU di lungo periodo—therefore, long-term permit of stay—and it’s usually unlimited, or “illimitata,” meaning it has no expiration date. You only need to make certain updates, like change the photos, update your address, your marital status or any other information that has changed. In the past you had to do that every 5 years, and now you need to do the update every 10 years.
Meanwhile, your initial Visa will have expired, and it’s the permesso di soggiorno that takes over as the legal document that allows you to stay in Italy. So your takeaway is: a Visa is just to enter a country and because of this, you must obtain it outside of Italy, in the Embassy or Consulate of Italy in your home country. The good thing is that you only need to do this once, as long as you stay in the same category. If you change from a student visa to work visa, for example, then of course you’ll need to apply all over again.