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

Yes

The word "parou" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. It is the third-person singular of the pretérito perfeito (simple past) of the verb parar. The only difference is in pronunciation. Brazilian Portuguese tends to have more open vowels and a more melodic, syllable-timed rhythm. In Continental Portuguese, vowels (especially unstressed ones) are often more closed or even reduced, and the rhythm is more stress-timed, which can subtly change the phonetic quality of the word.

Brazilian Portuguese Examples

1. O carro parou no sinal vermelho. (The car stopped at the red light.)
2. A chuva parou de repente. (The rain stopped suddenly.)
3. Ele parou de falar quando eu cheguei. (He stopped talking when I arrived.)
4. A máquina parou de funcionar ontem. (The machine stopped working yesterday.)
5. Ela parou de fumar mês passado. (She stopped smoking last month.)

Continental Portuguese Examples

1. O carro parou no semáforo. (The car stopped at the traffic light.)
2. A chuva parou num instante. (The rain stopped in an instant.)
3. Ele deixou de falar quando eu cheguei. (He stopped talking when I arrived.)
4. O motor parou de funcionar. (The engine stopped working.)
5. Ela deixou de fumar há algum tempo. (She stopped smoking some time ago.)