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

No

While the meaning, spelling, and conjugation of the word "sair" are identical in both dialects, there are differences in typical usage and pronunciation:

• Usage (Continuous Aspect): In Brazil, when expressing an action currently in progress, the gerund is used (e.g., saindo). In Portugal, the standard construction uses the preposition a followed by the infinitive (e.g., a sair).
• Pronunciation: Brazilian Portuguese tends to have more open, clearly articulated vowels. In Continental Portuguese, vowels (especially unstressed ones) are often reduced or "swallowed," making the "a" in "sair" sound much more closed and subtle.
• Syntactic Context: When using "sair" with possessives, Brazilians frequently omit the definite article (e.g., meus amigos), whereas Portuguese speakers almost always include it (e.g., os meus amigos).

Brazilian Portuguese Examples:

1. Eu estou saindo agora. (I am leaving now.)
2. O trem vai sair em breve. (The train will leave soon.)
3. Vamos sair com meus amigos. (Let's go out with my friends.)
4. Ele saiu de casa muito cedo. (He left home very early.)
5. O resultado vai sair amanhã. (The result will come out tomorrow.)

European Portuguese Examples:

1. Eu estou a sair agora. (I am leaving now.)
2. O comboio vai sair em breve. (The train will leave soon.)
3. Vamos sair com os meus amigos. (Let's go out with my friends.)
4. Ele saiu de casa muito cedo. (He left home very early.)
5. O resultado vai sair amanhã. (The result will come out tomorrow.)