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

Yes

The word "etapa" is identical in Brazilian and Continental Portuguese regarding its meaning (stage, phase, or leg of a journey), spelling, and grammatical gender (feminine). The only difference is in pronunciation: Brazilian Portuguese tends to have more open and clearly articulated vowels, whereas Continental Portuguese features significant vowel reduction, where unstressed vowels (like the "a" at the end of the word) are often shortened or pronounced more neutrally.

Brazilian Portuguese Examples

1. Esta é a última etapa do projeto. (This is the last stage of the project.)
2. A gente precisa terminar essa etapa logo. (We need to finish this stage soon.)
3. A primeira etapa do treinamento foi ótima. (The first stage of the training was great.)
4. Ele passou por uma etapa bem difícil. (He went through a very difficult stage.)
5. A próxima etapa do processo é a entrevista. (The next stage of the process is the interview.)

Continental Portuguese Examples

1. Esta é a última etapa do projeto. (This is the last stage of the project.)
2. Temos de concluir esta etapa brevemente. (We have to conclude this stage shortly.)
3. A primeira etapa do treino foi excelente. (The first stage of the training was excellent.)
4. Ele atravessou uma etapa complicada. (He went through a complicated stage.)
5. A etapa seguinte do processo é a entrevista. (The next stage of the process is the interview.)