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

No.

While the core meaning, spelling, and grammar of "atuar" are identical in both dialects, there is a difference in typical usage. In Brazilian Portuguese, "atuar" is very commonly used as a way to describe someone's professional field or activity (e.g., "working in marketing"). In Continental Portuguese, while "atuar" is used for acting in theater/cinema or for specific legal interventions, speakers more naturally use "trabalhar" (to work) or "desempenhar" (to perform/fulfill) when referring to general professional roles or employment.

Brazilian Portuguese Examples

1. Ele atua como advogado em grandes empresas. (He works as a lawyer in large companies.)
2. Ela atua na área de recursos humanos. (She works in the human resources area.)
3. O médico atua em uma clínica particular. (The doctor works in a private clinic.)
4. A empresa atua no mercado internacional. (The company operates in the international market.)
5. O professor atua no ensino fundamental. (The teacher works in elementary school.)

Continental Portuguese Examples

1. Ele trabalha como advogado em grandes empresas. (He works as a lawyer in large companies.)
2. Ela trabalha na área de recursos humanos. (She works in the human resources area.)
3. O médico trabalha numa clínica particular. (The doctor works in a private clinic.)
4. A empresa opera no mercado internacional. (The company operates in the international market.)
5. O professor trabalha no ensino básico. (The teacher works in primary school.)