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

Yes

The word "saia" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. It functions as a noun (meaning "skirt" or "the edge/skirt of an object like a mountain") and as the third-person singular present subjunctive of the verb sair (to leave/exit). The only difference is in pronunciation: in Brazilian Portuguese, the "ai" diphthong is typically more open and clearly articulated, whereas in Continental Portuguese, the vowels tend to be more closed or subject to greater reduction.

Brazilian Portuguese Examples

1. Ela comprou uma saia nova para a festa. (She bought a new skirt for the party.)
2. Não quero que ele saia de casa agora. (I don't want him to leave home now.)
3. Que saia justa eu passei naquela reunião! (What an awkward situation I went through in that meeting!)
4. A saia dela é muito comprida. (Her skirt is very long.)
5. É importante que a saia saia do lugar para ser lavada. (It is important that the skirt be moved from its place to be washed.)

Portuguese (Continental) Examples

1. Ela comprou uma saia de padrão. (She bought a patterned skirt.)
2. Não quero que ele saia sem o casaco. (I don't want him to leave without his coat.)
3. Que saia justa no trabalho! (What an awkward situation at work!)
4. A saia é de cor preta. (The skirt is black.)
5. Espero que ele saia a tempo do jantar. (I hope he leaves in time for dinner.)