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

Yes

The spelling, meaning, and grammatical functions of "estudante" are identical in both Brazilian and Continental Portuguese. The only difference is the pronunciation:

• Brazilian Portuguese: The word is pronounced with more open vowels, and the final "te" is typically palatalized, sounding like "tchi" (e.g., es-tu-DAN-tchi), especially in regions like Rio de Janeiro or São Paulo.
• Continental Portuguese: The vowels are more closed and reduced. The final "e" is often nearly silent or pronounced as a very short, neutral sound, making the word sound more like es-tu-DANT.

Brazilian Portuguese Examples

1. Eu sou estudante de medicina. (I am a medical student.)
2. O estudante está estudando muito para a prova. (The student is studying a lot for the test.)
3. Ela é uma estudante muito dedicada. (She is a very dedicated student.)
4. Os estudantes estão na biblioteca agora. (The students are in the library now.)
5. Como você é estudante, tem direito a meia-entrada. (Since you are a student, you are entitled to half-price.)

Continental Portuguese Examples

1. Eu sou estudante de medicina. (I am a medical student.)
2. O estudante está a estudar muito para o exame. (The student is studying a lot for the exam.)
3. Ela é uma estudante muito dedicada. (She is a very dedicated student.)
4. Os estudantes encontram-se na biblioteca agora. (The students are in the library now.)
5. Como tu és estudante, tens direito a desconto. (Since you are a student, you are entitled to a discount.)