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

Yes

The word is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only differences are phonological. In Brazilian Portuguese, the unstressed vowels are typically more open and clearly articulated, giving the word a more melodic, rhythmic quality. In Continental Portuguese, unstressed vowels are heavily reduced or "swallowed," making the word sound much more compressed. Additionally, the "s" at the end of the word is often pronounced as a "sh" sound [ʃ] in many regions of Portugal, whereas in much of Brazil, it is pronounced as a dental "s" [s].

Brazilian Portuguese

1. As rainhas do baile chegaram. (The queens of the ball arrived.)
2. Elas são as rainhas da festa. (They are the queens of the party.)
3. As rainhas da beleza desfilam hoje. (The beauty queens are parading today.)
4. Elas se sentem como rainhas com esse presente. (They feel like queens with this gift.)
5. As rainhas do Egito eram muito poderosas. (The queens of Egypt were very powerful.)

Continental Portuguese

1. As rainhas do baile chegaram. (The queens of the ball arrived.)
2. Elas são as rainhas da festa. (They are the queens of the party.)
3. As rainhas de beleza desfilam hoje. (The beauty queens are parading today.)
4. Elas sentem-se como rainhas com este presente. (They feel like queens with this gift.)
5. As rainhas do Egipto eram muito poderosas. (The queens of Egypt were very powerful.)