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

Yes

The word "porta" is identical in meaning, spelling, and grammatical gender in both Brazilian and European Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowels are generally more open, and the final "a" is pronounced clearly as [a]. In European Portuguese, unstressed final vowels are often "reduced" or swallowed, meaning the "a" in "porta" sounds much shorter and more neutral, almost like a muffled [ɐ].

Brazilian Portuguese Examples

1. Por favor, feche a porta. (Please, close the door.)
2. A porta do quarto está aberta. (The bedroom door is open.)
3. Eu bati na porta, mas não tinha ninguém. (I knocked on the door, but no one was there.)
4. Ele esqueceu a porta destrancada. (He left the door unlocked.)
5. A porta de entrada é de madeira. (The entrance door is made of wood.)

European Portuguese Examples

1. Por favor, fecha a porta. (Please, close the door.)
2. A porta do quarto está aberta. (The bedroom door is open.)
3. Bati à porta, mas não havia ninguém. (I knocked on the door, but there was no one.)
4. Ele deixou a porta destrancada. (He left the door unlocked.)
5. A porta de entrada é de madeira. (The entrance door is made of wood.)