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

Yes

The word "do" is a contraction of the preposition de (of/from) and the masculine singular article o (the). There are no differences in meaning, grammar, or spelling between Brazilian and Continental Portuguese. The only difference is in pronunciation:

• In Brazilian Portuguese, the "o" is typically pronounced more clearly and openly, often sounding like [du].
• In Continental Portuguese, the "o" is often reduced to a very short, unstressed sound or a schwa, sounding much closer to [d(u)].

Brazilian Portuguese Examples

1. Eu gosto do seu cachorro. (I like your dog.)
2. O sabor do sorvete é bom. (The flavor of the ice cream is good.)
3. O final do filme foi muito legal. (The end of the movie was very cool.)
4. Isso faz parte do meu plano. (This is part of my plan.)
5. O carro do meu irmão é azul. (My brother's car is blue.)

Continental Portuguese Examples

1. Gosto do teu cão. (I like your dog.)
2. O sabor do gelado é bom. (The flavor of the ice cream is good.)
3. O fim do filme foi muito fixe. (The end of the movie was very cool.)
4. Isso faz parte do meu plano. (This is part of my plan.)
5. O carro do meu irmão é azul. (My brother's car is blue.)