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

No.

While the spelling, grammar, and core meanings of "entrada" are identical in both dialects, there are differences in typical usage and pronunciation. In Brazilian Portuguese, "entrada" is the standard, primary term used to refer to a down payment on a purchase. In Continental Portuguese, while "entrada" can be used, the word "sinal" is much more common and natural for this purpose. Additionally, the pronunciation differs significantly: Brazilian Portuguese features more open vowels and a syllable-timed rhythm, whereas Continental Portuguese involves significant vowel reduction (where unstressed vowels become "closed" or nearly silent) and a more stress-timed rhythm.

Brazilian Portuguese

1. A entrada do prédio é por trás. (The building entrance is at the back.)
2. Eu dei uma entrada de mil reais no carro. (I gave a thousand reais down payment on the car.)
3. A entrada do restaurante estava ótima. (The restaurant appetizer was great.)
4. A entrada de usuários no sistema é lenta. (The entry of users into the system is slow.)
5. O valor da entrada é de cinquenta reais. (The entry fee is fifty reais.)

European Portuguese

1. A entrada do prédio é por trás. (The building entrance is at the back.)
2. Eu dei um sinal de mil euros no carro. (I gave a deposit of a thousand euros on the car.)
3. A entrada do restaurante estava ótima. (The restaurant appetizer was great.)
4. A entrada de utilizadores no sistema é lenta. (The entry of users into the system is slow.)
5. O valor do bilhete é de cinquenta euros. (The ticket price is fifty euros.)