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

Yes

The spelling, meaning, and grammar of the word "teatro" are identical in both Brazilian and European Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowels are more "open" and clearly articulated; the "e" in the first syllable is pronounced as a distinct, clear vowel (like /e/ or /ɛ/). In European Portuguese, unstressed vowels are much more "closed" or reduced. The "e" in "teatro" is often swallowed or reduced to a very short, almost silent sound, making the word sound more like "t'atro" (/tɐ'tɾatu/).

Brazilian Portuguese Examples

1. Eu gosto muito de ir ao teatro. (I like going to the theater very much.)
2. Ela está fazendo aulas de teatro. (She is taking theater classes.)
3. O teatro da nossa cidade é bem grande. (Our city's theater is quite big.)
4. Nós vamos assistir a uma peça de teatro hoje. (We are going to watch a theater play today.)
5. Ele trabalha como ator no teatro. (He works as an actor in the theater.)

European Portuguese Examples

1. Eu adoro ir ao teatro. (I love going to the theater.)
2. Ela está a fazer aulas de teatro. (She is taking theater classes.)
3. O teatro da nossa cidade é enorme. (Our city's theater is huge.)
4. Vamos ver uma peça de teatro hoje. (We are going to see a theater play today.)
5. Ele trabalha como ator no teatro. (He works as an actor in the theater.)