It helps to clarify terminology and use it carefully. There are no "visas" and thus no "student visa" or "work(ing) visa". "Visa" is a term we foreigners here tend to default to as a kind of jargon we are used to, but it confuses matters. In Argentina there are just "residences"
(residencias) and three categories thereof: (i)
transitoria (transitory), for just a few months, seemingly non-renewable and seemingly no DNI issued, (ii)
temporaria (temporary--for one year, and renewable for up to three, entailing also a DNI), and (iii)
permanente (permanent). The first two have sub-categories, e.g., in
temporaria there are, among others,
trabajador migrante (for coming to work, an as employee) and
estudiante (for coming to study). Two successive temporaries lead to permanent residency for Mercosur foreigners; for non-Mercosur, it is three successive
temporaries. There is also a
estudiante (student) sub-category in the
transitoria category, introduced in 2023 to cover newer types of short term study such as language programs, internships, exhanges. Anyone hoping to progress to permanent residency starting as a student will need to know which of the two student sub-categories they are in. And it needs to be the one in the
temporaria category. A language program sounds to be me like the
transitoria, which leads nowhere at the end except out of the country. The institution itself must know and be able to tell the candidate.
Start here:
https://www.argentina.gob.ar/migraciones/residencias
Then click on each of "Residencia Transitoria" and "Residencia Temporaria" to see the respective "Estudiante" sub-categories.
(Citizenship is a different category altogether. But let's get the basic concepts and language around
residencias clear first.)