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

Yes

The word "mapa" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference is in pronunciation:

• In Brazilian Portuguese, the vowels are more open and clearly articulated.
• In Continental Portuguese, unstressed vowels (especially the final "a") are often "reduced" or "closed," meaning they are pronounced much more softly, almost swallowed, or closer to a neutral "uh" sound.

Brazilian Portuguese examples:

1. Eu usei o mapa para achar o endereço. (I used the map to find the address.)
2. O mapa do metrô está no celular. (The subway map is on the cell phone.)
3. Você pode me mostrar o mapa? (Can you show me the map?)
4. Precisamos de um mapa para a trilha. (We need a map for the trail.)
5. O mapa indica que o caminho é longo. (The map indicates that the path is long.)

Continental Portuguese examples:

1. Usei o mapa para encontrar o endereço. (I used the map to find the address.)
2. O mapa do metro está no telemóvel. (The subway map is on the mobile phone.)
3. Podes mostrar-me o mapa? (Can you show me the map?)
4. Precisamos de um mapa para o trilho. (We need a map for the trail.)
5. O mapa indica que o caminho é longo. (The map indicates that the path is long.)