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

Yes

The only difference between "varanda" in Brazilian Portuguese and Continental Portuguese is pronunciation. In Brazilian Portuguese, the vowels are generally more open and clearly articulated. In Continental Portuguese, unstressed vowels tend to be more closed or "reduced," meaning they are pronounced with much less emphasis, which changes the phonetic rhythm of the word.

Brazilian Portuguese Examples

1. Eu adoro tomar café na varanda de manhã. (I love to drink coffee on the veranda in the morning.)
2. A nossa varanda tem muitas plantas. (Our veranda has many plants.)
3. Vamos sentar na varanda para ver o pôr do sol. (Let's sit on the veranda to watch the sunset.)
4. O cachorro está dormindo na varanda. (The dog is sleeping on the porch.)
5. Fizemos um churrasco na varanda no último domingo. (We had a barbecue on the veranda last Sunday.)

Continental Portuguese Examples

1. Adoro tomar café na varanda logo de manhã. (I love to drink coffee early in the morning on the veranda.)
2. A nossa varanda tem muitas plantas. (Our veranda has many plants.)
3. Vamos sentar na varanda para ver o pôr do sol. (Let's sit on the veranda to watch the sunset.)
4. O cão está a dormir na varanda. (The dog is sleeping on the porch.)
5. Fizemos um churrasco na varanda no domingo passado. (We had a barbecue on the veranda last Sunday.)