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

Yes

The word "tempestade" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference lies in pronunciation:

• Brazilian Portuguese: The pronunciation is more phonetic and "open." The final "e" is typically pronounced as a soft "dji" [dʒi].
• Continental Portuguese: The pronunciation is more "closed" or reduced. The vowels are often shortened, and the final "e" is often nearly silent or reduced to a very light, neutral sound [ɨ].

Brazilian Portuguese examples:

1. A tempestade causou muitos danos na cidade. (The storm caused a lot of damage in the city.)
2. Eu vi um raio durante a tempestade. (I saw lightning during the storm.)
3. A tempestade está chegando agora. (The storm is arriving now.)
4. Depois da tempestade, o sol apareceu. (After the storm, the sun appeared.)
5. O barulho da tempestade me assustou. (The noise of the storm scared me.)

Continental Portuguese examples:

1. A tempestade causou muitos estragos na cidade. (The storm caused a lot of damage in the city.)
2. Vi um raio durante a tempestade. (I saw lightning during the storm.)
3. A tempestade está a chegar agora. (The storm is arriving now.)
4. Após a tempestade, o sol apareceu. (After the storm, the sun appeared.)
5. O barulho da tempestade assustou-me. (The noise of the storm scared me.)