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

Yes

The word "cortina" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the vowels are generally more open and the rhythm is more melodic (syllable-timed). In Continental Portuguese, unstressed vowels are often "reduced" or nearly swallowed, making the word sound more clipped and consonant-heavy.

Brazilian Portuguese Examples

1. "Vou fechar a cortina porque o sol está muito forte." (I'm going to close the curtain because the sun is very strong.)
2. "Essa cortina da sala é de um tecido bem leve." (That living room curtain is made of a very light fabric.)
3. "Preciso lavar essas cortinas brancas." (I need to wash those white curtains.)
4. "A cortina de blackout ajuda a dormir melhor." (The blackout curtain helps to sleep better.)
5. "Ele puxou a cortina para ver o que estava acontecendo na rua." (He pulled the curtain to see what was happening in the street.)

Continental Portuguese Examples

1. "Vou fechar a cortina para o sol não entrar." (I'm going to close the curtain so the sun doesn't come in.)
2. "Esta cortina da sala é de um tecido muito leve." (This living room curtain is made of a very light fabric.)
3. "Preciso de lavar estas cortinas brancas." (I need to wash these white curtains.)
4. "A cortina de blackout ajuda a dormir melhor." (The blackout curtain helps to sleep better.)
5. "Ele puxou a cortina para ver o que se passava na rua." (He pulled the curtain to see what was happening in the street.)