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

Yes.

The word "traz" is identical in both Brazilian and Continental Portuguese regarding its meaning, spelling, and grammatical function; it is the third-person singular present indicative of the verb trazer (to bring). The only differences lie in pronunciation (specifically the vowel quality and rhythm) and the auxiliary vocabulary used in a sentence to express the same idea.

Brazilian Portuguese

1. Ele traz o lanche todo dia. (He brings the snack every day.)
2. O ônibus traz os estudantes. (The bus brings the students.)
3. A chuva traz alívio ao calor. (The rain brings relief to the heat.)
4. O caminhão traz a mercadoria. (The truck brings the merchandise.)
5. Ela traz o livro para casa. (She brings the book home.)

Continental Portuguese

1. Ele traz o lanche todos os dias. (He brings the snack every day.)
2. O autocarro traz os estudantes. (The bus brings the students.)
3. A chuva traz alívio ao calor. (The rain brings relief to the heat.)
4. O camião traz a mercadoria. (The truck brings the merchandise.)
5. Ela traz o livro para casa. (She brings the book home.)