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

No.

While the fundamental meanings (a financial institution, a bench/seat, or a school of fish), the spelling, and the grammar of the word "banco" are identical in both dialects, there are differences in typical usage and pronunciation.

• Typical Usage: In Brazil, the term "banco de dados" is the standard way to say "database." In Portugal, it is much more natural to use "base de dados." Similarly, in sports, a Brazilian would refer to the "banco de reserva" (the reserve bench), whereas a Portuguese person would naturally refer to the "banco de suplentes" (the substitute bench).
• Pronunciation: In Brazilian Portuguese, the pronunciation is more open and rhythmic, with a clear [u] sound for the unstressed "o." In Continental Portuguese, the unstressed syllables undergo significant reduction, making the word sound more clipped, with a much more closed and neutralized vowel sound.

Brazilian Portuguese Examples

1. Eu preciso ir ao banco pagar uma conta. (I need to go to the bank to pay a bill.)
2. O banco de dados está muito lento hoje. (The database is very slow today.)
3. Vamos sentar naquele banco de madeira. (Let's sit on that wooden bench.)
4. O jogador ficou no banco de reserva. (The player stayed on the reserve bench.)
5. Avistamos um grande banco de peixes. (We spotted a large school of fish.)

Continental Portuguese Examples

1. Eu preciso ir ao banco pagar uma conta. (I need to go to the bank to pay a bill.)
2. A base de dados está muito lenta hoje. (The database is very slow today.)
3. Vamos sentar naquele banco de madeira. (Let's sit on that wooden bench.)
4. O jogador ficou no banco de suplentes. (The player stayed on the substitute bench.)
5. Avistamos um grande banco de peixes. (We spotted a large school of fish.)