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

Yes

The word "ensinar" is identical in both Brazilian and European Portuguese regarding its meaning, spelling, and grammatical conjugation. The only difference lies in pronunciation. In Brazil, vowels are typically more open and clearly articulated, even in unstressed syllables. In Portugal, vowels tend to be much more "closed" or "reduced," meaning unstressed vowels are often swallowed or barely pronounced, giving the language a more consonant-heavy, rhythmic sound.

Brazilian Portuguese Examples

1. Eu vou te ensinar a dirigir. (I am going to teach you how to drive.)
2. Ela ensina matemática na escola. (She teaches math at school.)
3. Você pode me ensinar a fazer esse bolo? (Can you teach me how to make this cake?)
4. Ele está ensinando inglês para os alunos. (He is teaching English to the students.)
5. Me ensina a jogar videogame? (Teach me how to play video games?)

European Portuguese Examples

1. Eu vou ensinar-te a conduzir. (I am going to teach you how to drive.)
2. Ela ensina matemática na escola. (She teaches math at school.)
3. Podes ensinar-me a fazer este bolo? (Can you teach me how to make this cake?)
4. Ele está a ensinar inglês aos alunos. (He is teaching English to the students.)
5. Queres ensinar-me a jogar videojogos? (Do you want to teach me how to play video games?)