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

Yes

The word "reserva" is identical in spelling, grammar, and fundamental meaning in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, vowels are more open and clearly articulated. In Continental Portuguese, unstressed vowels are often reduced or "swallowed" (a phenomenon called vowel reduction), which makes the word sound more clipped and less rhythmic.

Brazilian Portuguese Examples

1. Eu fiz uma reserva no restaurante para as oito. (I made a reservation at the restaurant for eight o'clock.)
2. Ele é um cara muito reservado. (He is a very reserved guy.)
3. É importante ter uma reserva de emergência. (It is important to have an emergency fund.)
4. A reserva de água está baixando muito. (The water reserve is dropping a lot.)
5. Você já confirmou a sua reserva? (Have you already confirmed your reservation?)

Continental Portuguese Examples

1. Fiz uma reserva no restaurante para as oito. (I made a reservation at the restaurant for eight o'clock.)
2. Ele é um homem muito reservado. (He is a very reserved man.)
3. É importante ter uma poupança para emergências. (It is important to have savings for emergencies.)
4. A reserva de água está a baixar muito. (The water reserve is dropping a lot.)
5. Já confirmaste a tua reserva? (Have you confirmed your reservation?)