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

Yes

The word "molhada" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, vowels are generally more "open" and clearly articulated. In Continental Portuguese, unstressed vowels (such as the final "a") are often "reduced" or "swallowed," making the word sound more closed or clipped.

Brazilian Portuguese usage

1. Minha roupa ficou toda molhada por causa da chuva. (My clothes got all wet because of the rain.)
2. A calçada está muito molhada. (The sidewalk is very wet.)
3. Não saia com o cabelo molhado. (Don't go out with wet hair.)
4. A terra do vaso está bem molhada. (The soil in the pot is very wet.)
5. Minha mão está molhada de suor. (My hand is wet with sweat.)

Continental Portuguese usage

1. A minha roupa ficou toda molhada com a chuva. (My clothes got all wet with the rain.)
2. O passeio está muito molhado. (The pavement is very wet.)
3. Não vás com o cabelo molhado. (Don't go with wet hair.)
4. A terra do vaso está bastante molhada. (The soil in the pot is quite wet.)
5. A minha mão está molhada de suor. (My hand is wet with sweat.)