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

Yes

The word "atua" (the third-person singular present indicative of the verb atuar) is identical in meaning, grammar, and spelling in both Brazilian and Continental Portuguese. The only difference lies in pronunciation.

In Brazilian Portuguese, the unstressed vowels (the "a" at the beginning and the end) are typically more open and clearly articulated. In Continental Portuguese, unstressed vowels undergo "vowel reduction," meaning they are pronounced much more softly, are more closed, or may almost disappear entirely, making the word sound shorter and more compressed.

Brazilian Portuguese Examples

1. Ele atua como advogado em São Paulo. (He works as a lawyer in São Paulo.)
2. A atriz atua muito bem neste filme. (The actress acts very well in this movie.)
3. O remédio atua diretamente na dor. (The medicine acts directly on the pain.)
4. A empresa atua em diversos setores. (The company operates in various sectors.)
5. O governo atua para reduzir a pobreza. (The government acts to reduce poverty.)

Continental Portuguese Examples

1. Ele exerce a profissão de advogado em Lisboa. (He practices the profession of lawyer in Lisbon.)
2. A atriz interpreta muito bem este papel. (The actress plays this role very well.)
3. Este medicamento atua no sistema nervoso. (This medication acts on the nervous system.)
4. A empresa opera em diversos setores. (The company operates in various sectors.)
5. O governo intervém para combater a pobreza. (The government intervenes to combat poverty.)