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

Yes

The word "jogo" is identical in meaning, spelling, and grammar in both Brazilian and European Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the vowels are generally more open and the word is pronounced with a clearer, more melodic cadence. In Continental (European) Portuguese, the vowels are much more closed, and unstressed vowels (like the final "o") are often reduced or almost swallowed, making the word sound more "clipped."

Brazilian Portuguese Examples

1. Eu jogo videogame todo fim de semana. (I play video games every weekend.)
2. O jogo de futebol foi cancelado por causa da chuva. (The football match was cancelled because of the rain.)
3. Este jogo de tabuleiro é muito difícil. (This board game is very difficult.)
4. Eu jogo cartas com meu avô. (I play cards with my grandfather.)
5. O jogo de hoje vai ser emocionante. (Today's game is going to be exciting.)

European Portuguese Examples

1. Eu jogo na consola todos os fins de semana. (I play on the console every weekend.)
2. O jogo de futebol foi cancelado devido à chuva. (The football match was cancelled due to the rain.)
3. Este jogo de tabuleiro é muito difícil. (This board game is very difficult.)
4. Eu jogo às cartas com o meu avô. (I play cards with my grandfather.)
5. O jogo de hoje vai ser emocionante. (Today's game is going to be exciting.)