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

No

While the spelling and meaning of "ensina" are identical in both dialects, the answer is No because there are significant differences in typical usage and the grammatical construction surrounding the word. In Brazilian Portuguese, it is natural to use proclisis (placing the object pronoun before the verb, e.g., "me ensina"), whereas in European Portuguese, enclisis (placing the pronoun after the verb, e.g., "ensina-me") is the standard. Additionally, the vocabulary used in the same sentence often differs (e.g., "dirigir" vs. "conduzir").

Brazilian Portuguese Usage

1. Ele me ensina muito bem. (He teaches me very well.)
2. Meu pai me ensina a dirigir. (My father teaches me how to drive.)
3. Ela ensina inglês para crianças. (She teaches English to children.)
4. O professor ensina a matéria de um jeito fácil. (The teacher teaches the subject in an easy way.)
5. O guia ensina o caminho de um jeito claro. (The guide teaches the way in a clear way.)

Continental Portuguese Usage

1. Ele ensina-me muito bem. (He teaches me very well.)
2. O meu pai ensina-me a conduzir. (My father teaches me how to drive.)
3. Ela ensina Inglês a crianças. (She teaches English to children.)
4. O professor ensina a matéria de uma forma simples. (The teacher teaches the subject in a simple way.)
5. O guia ensina o caminho de uma forma clara. (The guide teaches the way in a clear way.)