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

Yes

The differences between the use of "peça" in Brazilian and Continental Portuguese are strictly phonetic. In Brazilian Portuguese, the vowels are typically more open and clearly articulated. In Continental Portuguese, there is a significant phenomenon of vowel reduction, where unstressed vowels (such as the final "a" in "peça") are pronounced as much more closed, shortened, or even nearly silent sounds. The spelling, grammar, and fundamental meanings—such as a theater play, a component of a machine, an item of clothing, or the subjunctive form of the verb pedir (to ask/request)—are identical in both dialects.

Brazilian Portuguese Examples:

1. "Eu adorei essa peça de teatro." (I loved that play.)
2. "O mecânico está trocando a peça do motor." (The mechanic is changing the engine part.)
3. "Esta peça de roupa é muito bonita." (This item of clothing is very beautiful.)
4. "Essa peça do quebra-cabeça sumiu." (That puzzle piece went missing.)
5. "Ele é uma peça muito engraçada." (He is a very funny/quirky person.)

Portuguese (Portugal) Examples:

1. "Eu adorei esta peça de teatro." (I loved this play.)
2. "O mecânico está a trocar a peça do motor." (The mechanic is changing the engine part.)
3. "Esta peça de roupa é muito bonita." (This item of clothing is very beautiful.)
4. "Essa peça do puzzle desapareceu." (That puzzle piece disappeared.)
5. "Ele é uma peça muito engraçada." (He is a very funny/quirky person.)