Vestibular vs. exame de admissão
While both terms translate to entrance exam, the difference relies heavily on regional usage (Brazil vs. Portugal) and the specific level of education involved. Vestibular is undoubtedly the most common term in Brazil for university entry, whereas exame de admissão is a broader, descriptive term used in Portugal or for other types of institutions.
Vestibular
B1This word is exclusively used in Brazil to refer to the competitive entrance examinations for colleges and universities. It is a cultural institution in Brazil, and the term is not used in Portugal or other Portuguese-speaking countries.
O meu irmão está estudando muito para o vestibular de medicina.
(My brother is studying hard for the medical school entrance exam.)
As datas do vestibular foram alteradas este ano.
(The university entrance exam dates were changed this year.)
Passar no vestibular é o sonho de muitos estudantes brasileiros.
(Passing the university entrance exam is the dream of many Brazilian students.)
Ela fez um cursinho para se preparar para o vestibular.
(She took a prep course to prepare for the university entrance exam.)
Exame de admissão
B2This is the literal translation of admission exam. It is the standard term used in Portugal for university entry. In Brazil, it is a general term used for private schools, professional guilds, or historically for old middle school exams, but rarely for modern universities.
Em Portugal, os alunos realizam um exame de admissão para entrar na universidade.
(In Portugal, students take an entrance exam to get into university.)
A escola particular exige um exame de admissão para novos alunos.
(The private school requires an entrance exam for new students.)
Meu avô sempre conta histórias do seu exame de admissão para o ginásio.
(My grandfather always tells stories about his admission exam for middle school.)
O clube exige um rigoroso exame de admissão para novos sócios.
(The club requires a rigorous admission exam for new members.)
Summary
Use vestibular only when talking about entering a university in a Brazilian context. Use exame de admissão for university exams in Portugal, for entrance tests for private schools/clubs, or when speaking generally about the concept of being admitted to an institution.