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

Yes

The word "corte" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is in pronunciation:

• In Brazilian Portuguese, the final, unstressed "e" is typically pronounced as a high, closed vowel, sounding like the "ee" in "see" (/ˈkɔɾtʃi/ or /ˈkɔɾti/).
• In Continental Portuguese, the final "e" is much more reduced, often becoming a nearly silent, extremely short vowel (a schwa), making the word sound closer to "kort" (/ˈkɔɾt/).

Brazilian Portuguese Examples

1. Eu preciso de um novo corte de cabelo. (I need a new haircut.)
2. O governo anunciou um corte de gastos. (The government announced a spending cut.)
3. A corte decidiu o veredito. (The court decided the verdict.)
4. Ele teve um corte profundo no braço. (He had a deep cut on his arm.)
5. Este é um bom corte de carne. (This is a good cut of meat.)

Continental Portuguese Examples

1. Eu preciso de um novo corte de cabelo. (I need a new haircut.)
2. O governo anunciou um corte de verbas. (The government announced a budget cut.)
3. O tribunal decidiu o veredito. (The court decided the verdict.)
4. Ele teve um corte profundo no braço. (He had a deep cut on his arm.)
5. Este é um bom corte de carne. (This is a good cut of meat.)