School + University Institute (or Faculty + University School)
Let me say that I agree in general terms with Taña's comments, and I think that it would be quite legitimate to put "Faculty of Medicine" and call the Escuela Universitaria a "University School" (as perhaps one usually would). Of course, I agree with you, Mónica, that using "School" for both would be confusing.
However, although you could use "Faculty", I think the argument for using "School of Medicine" is strong. It's been the standard term in the US for a long time. Of course, as with "Law School", a medical school is a graduate school: people who enter already have a bachelor's degree (at least as a rule).
In the UK, in my day (over twenty years ago), they were normally called Faculties of Medicine, and they still are in a minority of universities. I can't speak for Ireland back then, but I strongly suspect the same was true there. Nowadays, however, all or nearly all Irish universities have Schools of Medicine, though they still have Faculties of other things, and a large majority of universities in the UK do as well, even though Medicine is generally an undergraduate degree subject. So I think the natural translation is indeed "School of Medicine".
So what do we do with "Escuela Universitaria"? I am not really happy with department or division, which are standard terms for a subdivision of a faculty. I don't think an "escuela universitaria" is the same kind of body as a "departamento": it's more than that. It suggests a kind of semi-autonomous body within the Faculty (or School).
I'm a great believer in trying to find out the nature of the body in question, where possible, and here it's easy:
"La Escuela Universitaria de Tecnología Médica (EUTM) de Uruguay, forma parte de la Universidad de la República (UdelaR) y concretamente de la Facultad de Medicina (Universidad de la República); teniendo dos sedes en el país, una en el departamento de Montevideo y la segunda en el departamento de Paysandú. [...]
El instituto fue fundado por el Dr. Mario Cassinoni en la ciudad de Montevideo en la década del '50. Hace treinta y cinco años la EUTM se encuentra brindando formación en Paysandú, formando parte del Centro Universitario de Paysandú —como se mencionó anteriormente—; donde se dictaron en principio los cursos de Fisioterapia, Hemoterapia, Radiología, Archivo médico, y Laboratorio clínico."
The EUTM does not simply supply teaching for the School of Medicine in various subjects in the medical degree programme; it offers 18 licenciaturas of its own.
I think you could call this a university institute. The objection to this term might be that it often implies a research institute, for graduates, but this is not always so: Institutes of Education, for example, which normally form part of universities, also run undergraduate degree courses:
In Ireland, an Institute of Technology is typically a tertiary university-equivalent institution running undergraduate and graduate degree courses. It is not typically part of a university, but in principle it could be. I think this is the best alternative to "School" here.
The EUTM is listed here as one of the "Schools and Institutes" of the University of the Republic:
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