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

Yes

The word "muçulmana" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. It refers to a female follower of Islam. The only difference lies in pronunciation. In Brazilian Portuguese, the vowels are more open and the unstressed syllables are pronounced more clearly. In Continental Portuguese, vowels that are not stressed (such as the "u" in the first syllable) tend to be more closed, reduced, or even almost silent, resulting in a more rhythmic, consonant-heavy sound.

Brazilian Portuguese Examples

1. Ela é uma mulher muçulmana muito dedicada. (She is a very dedicated Muslim woman.)
2. A comunidade muçulmana cresceu bastante na nossa cidade. (The Muslim community has grown quite a bit in our city.)
3. Ela usa o véu por ser muçulmana. (She wears the veil because she is Muslim.)
4. Minha amiga muçulmana não come carne de porco. (My Muslim friend does not eat pork.)
5. Ela está estudando muito sobre a cultura muçulmana. (She is studying a lot about Muslim culture.)

Continental Portuguese Examples

1. Ela é uma mulher muçulmana muito dedicada. (She is a very dedicated Muslim woman.)
2. A comunidade muçulmana cresceu muito na cidade. (The Muslim community has grown a lot in the city.)
3. Ela usa o véu por ser muçulmana. (She wears the veil because she is Muslim.)
4. A minha amiga muçulmana não come porco. (My Muslim friend does not eat pork.)
5. Ela estuda a cultura muçulmana há anos. (She has been studying Muslim culture for years.)