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

No

While "joga" (the third-person singular of the verb jogar) shares the same spelling and the core meaning of "plays" (in the context of games or sports) in both dialects, there is a significant difference in typical usage. In Brazil, "joga" is commonly used as a synonym for "throws" (e.g., joga a bola). In Portugal, however, the verb jogar is almost exclusively reserved for games and sports; a Portuguese person would rarely use "joga" to mean "throws," instead opting for verbs like atira, lança, or deita.

Brazilian Portuguese

1. Ele joga futebol todos os dias. (He plays soccer every day.)
2. Joga a bola para o cachorro. (Throw the ball to the dog.)
3. Ela joga muito bem no videogame. (She plays video games very well.)
4. Joga esse papel no lixo. (Throw this paper in the trash.)
5. O menino joga cartas com o amigo. (The boy plays cards with his friend.)

Portuguese (Portugal)

1. Ele joga futebol todos os dias. (He plays soccer every day.)
2. Atira a bola para o cão. (Throw the ball to the dog.)
3. Ela joga muito bem no videogame. (She plays video games very well.)
4. Deita esse papel no lixo. (Throw this paper in the trash.)
5. O menino joga cartas com o amigo. (The boy plays cards with his friend.)