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

Yes

The word "entrar" is identical in meaning, grammar, and spelling in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. Brazilian Portuguese is a more "vocalic" dialect, meaning the vowels are generally more open and clearly articulated. In Continental Portuguese, the pronunciation is more "consonantal"; unstressed vowels are often reduced, shortened, or almost swallowed, making the word sound more clipped or compressed to a Brazilian ear.

Brazilian Portuguese Examples

1. Eu vou entrar na sala agora. (I am going to enter the room now.)
2. Você pode entrar, a porta está aberta. (You can come in, the door is open.)
3. Ele quer entrar no curso de medicina. (He wants to enter/start medical school.)
4. Vamos entrar em contato com ele amanhã. (We will get in touch with him tomorrow.)
5. O cachorro entrou no quintal. (The dog entered the backyard.)

Continental Portuguese Examples

1. Eu vou entrar na sala agora. (I am going to enter the room now.)
2. Pode entrar, a porta está aberta. (You can come in, the door is open.)
3. Ele quer entrar no curso de medicina. (He wants to enter/start medical school.)
4. Vamos entrar em contacto com ele amanhã. (We will get in touch with him tomorrow.)
5. O cão entrou no quintal. (The dog entered the backyard.)