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

Yes

The word "gerente" is identical in spelling, meaning, and grammar in both Brazilian and European Portuguese. The only difference lies in pronunciation:

• Brazilian Portuguese: The final "e" is typically pronounced clearly, sounding like a soft "ee" (as in "tree") or a light "eh."
• European Portuguese: The final "e" is highly reduced and often becomes almost silent or sounds like a very short, muted "uh" ([ɨ]). Additionally, the rhythm of the word is more stressed on the penultimate syllable, with the unstressed vowels being much shorter than in Brazil.

Brazilian Portuguese Examples

1. Eu preciso falar com o gerente agora. (I need to speak with the manager now.)
2. O gerente do banco foi muito atencioso comigo. (The bank manager was very helpful to me.)
3. Ela foi promovida a gerente de vendas ontem. (She was promoted to sales manager yesterday.)
4. O gerente da loja está de folga hoje. (The store manager is off today.)
5. Precisamos reportar este problema diretamente ao gerente. (We need to report this problem directly to the manager.)

European Portuguese Examples

1. Gostaria de falar com o gerente, por favor. (I would like to speak with the manager, please.)
2. O gerente da unidade encontra-se em reunião. (The unit manager is in a meeting.)
3. Fui ao banco para tratar de um assunto com o gerente de conta. (I went to the bank to deal with a matter with the account manager.)
4. O gerente da loja deu-me um desconto especial. (The store manager gave me a special discount.)
5. Deves apresentar a tua queixa ao gerente. (You should present your complaint to the manager.)