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

Yes.

The word "sai" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. It serves as the third-person singular present indicative of the verb sair (to leave, to exit, to emerge) and the second-person singular imperative (a command to "leave"). The only difference is pronunciation: in Brazilian Portuguese, the "a" is typically more open and the rhythm is more melodic, whereas in Continental Portuguese, the "a" can be more closed or neutralized depending on the regional accent.

Brazilian Portuguese Examples

1. Ele sai de casa muito cedo. (He leaves home very early.)
2. Sai daqui agora mesmo! (Get out of here right now!)
3. O resultado do exame sai amanhã. (The exam result comes out tomorrow.)
4. Ela sai com os amigos todo final de semana. (She goes out with friends every weekend.)
5. Quando o sol sai, o calor aumenta. (When the sun comes out, the heat increases.)

Portuguese (Portugal) Examples

1. Ele sai de casa muito cedo. (He leaves home very early.)
2. Sai daqui agora mesmo! (Get out of here right now!)
3. O resultado do exame sai amanhã. (The exam result comes out tomorrow.)
4. Ela sai com os amigos todos os fins de semana. (She goes out with friends every weekend.)
5. Quando o sol sai, o calor aumenta. (When the sun comes out, the heat increases.)