The early European "university" was called Studium Generale (and sometimes Studium Universale or Studium Commune). The term universitas was used to refer to associations of students, essentially guilds, from the same geographical area. The Studium Generale in Bologna had originally two major guilds, Universitas Citramontarum and Universitas Ultramontanorum, respectively for Italian and non-Italian students, each further subdivided into "nations" of students from the same country or region. They were essentially powerful unions of students. At this time students in a Studium Generale would have been tonsured religious men, with ecclesiastical benefices (stipends from the Church), not what we associate today with university students. In some of the Studium Universale, for example Paris, there were universitas that formed the guild of the teachers, rather than the students. But in all cases, the term universitas was not the term used to talk about the school itself, but rather a group of students or teachers within it. Over time, the universitas changed from a focus on geography to one on subjects. By the 15th century, Bologna had two universitas, one for Law and the other for Arts and Medicine, which were still associations of students. Eventually the term universitas associated with the guild of students studying a subject became associated with the school that was teaching those subjects, and that is where the modern term university comes from.

Source: Robert S. Rail, Life in the medieval university, Cambridge University Press