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

Yes

The word "corpo" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the final "o" is typically pronounced as a clear, closed [u] sound. In Continental Portuguese, the reduction of unstressed vowels is much more extreme; the final "o" is often very short or "swallowed," creating a more "clipped" or "staccato" rhythmic effect.

Brazilian Portuguese Examples:

1. Eu preciso cuidar mais do meu corpo. (I need to take more care of my body.)
2. O corpo de bombeiros foi chamado para o acidente. (The fire department was called to the accident.)
3. Ela tem um corpo muito forte. (She has a very strong body.)
4. O corpo docente da escola é excelente. (The school's faculty is excellent.)
5. Sinto uma dor no corpo todo. (I feel a pain in my whole body.)

Portuguese (Continental) Examples:

1. Eu preciso de cuidar melhor do meu corpo. (I need to take better care of my body.)
2. Os bombeiros foram chamados para o acidente. (The firefighters were called to the accident.)
3. Ela tem um corpo muito forte. (She has a very strong body.)
4. O corpo docente da escola é excelente. (The school's faculty is excellent.)
5. Sinto uma dor no corpo inteiro. (I feel a pain in my whole body.)