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

Yes

The spelling, meaning, and grammatical function of the word "jazz" are identical in both Brazilian and Continental Portuguese. The only difference lies in pronunciation.

In Brazilian Portuguese, the "z" at the end of the word is typically pronounced clearly as a voiced /z/, and the vowels are more open. In Continental Portuguese, the pronunciation is more closed, and the final "z" can sometimes be neutralized or sound more like a soft "sh" (/ʃ/) depending on the speaker's regional accent and the phonetic environment.

Brazilian Portuguese Examples

1. Eu adoro ouvir jazz para relaxar. (I love listening to jazz to relax.)
2. O show de jazz foi muito legal. (The jazz show was very cool.)
3. Ele toca jazz muito bem no saxofone. (He plays jazz very well on the saxophone.)
4. Tem uma banda de jazz tocando ali. (There is a jazz band playing over there.)
5. Eu gosto de estudar ouvindo jazz. (I like to study listening to jazz.)

Continental Portuguese Examples

1. Eu adoro ouvir jazz para relaxar. (I love listening to jazz to relax.)
2. O concerto de jazz foi muito fixe. (The jazz concert was very cool.)
3. Ele toca jazz muito bem no saxofone. (He plays jazz very well on the saxophone.)
4. Há uma banda de jazz a tocar ali. (There is a jazz band playing there.)
5. Eu gosto de estudar a ouvir jazz. (I like to study listening to jazz.)