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

No

While the spelling and fundamental meaning of "vai" (the third-person singular of the verb ir) are identical, there is a difference in typical usage. In Brazilian Portuguese, "vai" is the primary way to express the near future through the construction ir + infinitive (e.g., vai fazer). In Continental Portuguese, while this construction is used, the simple future tense (e.g., fará) is much more prevalent in standard speech. Additionally, "vai" is frequently used in Brazil as an informal interjection of encouragement, whereas a Portuguese person would more naturally use "força" or "anda."

Brazilian Portuguese Examples

1. Ele vai chegar tarde hoje. (He is going to arrive late today.)
2. Vai dar tudo certo. (Everything is going to work out.)
3. Você vai estudar para a prova? (Are you going to study for the test?)
4. Vai, você consegue! (Go, you can do it!)
5. O ônibus vai passar logo. (The bus is going to pass soon.)

Continental Portuguese Examples

1. Ele chegará tarde hoje. (He will arrive late today.)
2. Tudo correrá bem. (Everything will go well.)
3. Vais estudar para o exame? (Are you going to study for the exam?)
4. Força, tu consegues! (Go/Strength, you can do it!)
5. O autocarro passará em breve. (The bus will pass soon.)