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

Yes

The spelling, meaning, and grammatical function of "professora" are identical in both Brazilian and Continental Portuguese. The only significant difference is pronunciation.

In Brazilian Portuguese, the word is pronounced with "open" and clearly articulated vowels. For example, the unstressed "e" is typically pronounced as an open /ɛ/ (like the "e" in "get"). In Continental Portuguese, the word undergoes "vowel reduction." The unstressed vowels are much more "closed" or "clipped," often sounding almost swallowed or nearly disappearing entirely (the "e" might sound like a very short /ɨ/ or /e/).

Brazilian Portuguese Examples

1. A professora explicou a matéria de um jeito fácil. (The teacher explained the subject in an easy way.)
2. Eu gosto muito da minha professora de matemática. (I like my math teacher very much.)
3. A professora deu muita lição de casa hoje. (The teacher gave a lot of homework today.)
4. A professora falou para a gente ficar quieto. (The teacher told us to be quiet.)
5. Preciso entregar esse trabalho para a professora. (I need to hand this assignment to the teacher.)

Portuguese (Portugal) Examples

1. A professora explicou a matéria de forma simples. (The teacher explained the subject in a simple way.)
2. Gosto muito da minha professora de matemática. (I like my math teacher very much.)
3. A professora deu muito trabalho de casa hoje. (The teacher gave a lot of homework today.)
4. A professora disse para ficarmos quietos. (The teacher told us to be quiet.)
5. Tenho de entregar este trabalho à professora. (I have to hand this assignment to the teacher.)