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

Yes

The word "volta" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the vowels are generally more open and clearly articulated. In Continental Portuguese, unstressed vowels are often reduced or "closed," meaning the "o" in volta is much shorter and more neutralized, sounding closer to a swallowed "u."

Brazilian Portuguese

1. Vamos dar uma volta no shopping? (Let's go for a stroll in the mall?)
2. A volta do ônibus demorou muito. (The return of the bus took a long time.)
3. Ele deu uma volta de carro para relaxar. (He took a car ride to relax.)
4. Ele venceu na última volta da corrida. (He won on the last lap of the race.)
5. A tomada de casa é de 110 volts. (The house outlet is 110 volts.)

Continental Portuguese

1. Vamos dar uma volta ao centro comercial? (Let's go for a stroll to the shopping center?)
2. A volta do autocarro demorou muito. (The return of the bus took a long time.)
3. Ele deu uma volta de carro para descontrair. (He took a car ride to unwind.)
4. Ele venceu na última volta da corrida. (He won on the last lap of the race.)
5. A tomada de casa é de 230 volts. (The house outlet is 230 volts.)