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

Yes

The spelling, meaning, and grammatical category (feminine noun) of the word "chuva" are identical in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. Brazilian Portuguese tends to have more open vowels and follows a syllable-timed rhythm, making the word sound more "even." In Continental Portuguese, unstressed vowels are often reduced or shortened, and the rhythm is more stress-timed, which can make the "a" at the end of the word sound more neutralized or clipped.

Brazilian Portuguese Examples

1. A chuva está muito forte hoje. (The rain is very strong today.)
2. Eu peguei muita chuva no caminho para o trabalho. (I got very rained on on my way to work.)
3. Tem previsão de chuva para o final de semana. (There is a forecast of rain for the weekend.)
4. A chuva parou agora pouco. (The rain stopped a little while ago.)
5. Eu adoro o cheiro de terra molhada depois da chuva. (I love the smell of wet earth after the rain.)

Continental Portuguese Examples

1. A chuva está a cair com muita força hoje. (The rain is falling very hard today.)
2. Eu apanhei muita chuva no caminho para o trabalho. (I got very rained on on my way to work.)
3. Há previsão de chuva para o fim de semana. (There is a forecast of rain for the weekend.)
4. A chuva parou há pouco. (The rain stopped a little while ago.)
5. Eu adoro o cheiro de terra molhada depois da chuva. (I love the smell of wet earth after the rain.)