Is there any update on this? What exactly is an 'Institute' in English? (And which English are you using?)
To me (Hiberno-English and British-English) my guess would either be an Institute of Technology or Polytech, or a High-School or Sitxh-Form, but I'm really not sure.
Is it the same as the French 'Lycée' ? When I French -> Spanish translate 'Lycée' I get 'Colegio' or 'Escuela Secundaria'.
Institute and institution have different meaning.
Institute is an organization.
Institution is a building.
Take a look in the examples:
We study in the same institute.
Estudiamos en el mismo instituto.
We study in the same institution.
Estudiamos en la misma institución.