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

Yes

The word "casa" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the vowels are typically more open and clearly articulated. In Continental Portuguese, there is a significant "vowel reduction," meaning unstressed vowels (such as the final "a") are often pronounced more closed, shortened, or even swallowed, making the word sound much more clipped.

Brazilian Portuguese examples:

1. Eu vou para casa agora. (I am going home now.)
2. Minha casa é muito bonita. (My house is very beautiful.)
3. Você quer vir aqui em casa? (Do you want to come to my house?)
4. A casa dele é longe daqui. (His house is far from here.)
5. Estou limpando a casa toda. (I am cleaning the whole house.)

Portuguese (Portugal) examples:

1. Eu vou para casa agora. (I am going home now.)
2. A minha casa é muito bonita. (My house is very beautiful.)
3. Queres vir cá a casa? (Do you want to come to my house?)
4. A casa dele é longe daqui. (His house is far from here.)
5. Estou a limpar a casa toda. (I am cleaning the whole house.)