Is the word biblioteca the same in Brazilian and European Portuguese?

Yes

The word "biblioteca" has the exact same meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. It refers to a library (a place where books are kept/borrowed) or a collection of books. The only difference lies in pronunciation:

• Brazilian Portuguese: The vowels in unstressed syllables are more "open" and clearly articulated.
• Continental Portuguese: The vowels in unstressed syllables undergo significant reduction, often sounding much shorter, more "closed," or almost swallowed (a phenomenon known as vowel reduction).

Brazilian Portuguese Examples

1. Eu estou estudando na biblioteca. (I am studying in the library.)
2. A biblioteca da minha escola é muito grande. (My school's library is very large.)
3. Você viu onde está o livro da biblioteca? (Did you see where the library book is?)
4. Eu preciso devolver este livro na biblioteca hoje. (I need to return this book to the library today.)
5. A biblioteca está fechada agora. (The library is closed now.)

Continental Portuguese Examples

1. Estou a estudar na biblioteca. (I am studying in the library.)
2. A biblioteca da minha escola é muito grande. (My school's library is very large.)
3. Viste onde está o livro da biblioteca? (Did you see where the library book is?)
4. Tenho de devolver este livro à biblioteca hoje. (I have to return this book to the library today.)
5. A biblioteca encontra-se fechada agora. (The library is closed now.)