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

No

While the spelling, grammar, and most core meanings (such as social strata, categories, or elegance) are identical, there is a difference in typical usage and pronunciation:

• Usage: In Brazil, "classe" is frequently used as a synonym for "turma" to refer to a specific group of students (e.g., "the 5th-grade class"). In Portugal, "classe" is much more strictly reserved for social or categorical contexts, whereas "turma" is the standard and natural word for a group of students.
• Pronunciation: In Brazilian Portuguese, the final "e" is pronounced as a closed "i" (/ˈklas.si/). In Continental Portuguese, the final "e" is a reduced, near-silent vowel, often sounding like a schwa (/ˈklas/).

Brazilian Portuguese Examples

1. Ela é uma mulher de muita classe. (She is a woman of great class/elegance.)
2. A classe social é um tema central na sociologia. (Social class is a central theme in sociology.)
3. Esta é uma nova classe de medicamentos. (This is a new class of medication.)
4. A classe de ballet está muito animada hoje. (The ballet class/group is very excited today.)
5. O professor organizou a classe de alunos. (The teacher organized the class of students.)

Continental Portuguese Examples

1. Ela é uma mulher de muita classe. (She is a woman of great class/elegance.)
2. A classe social é um tema central na sociologia. (Social class is a central theme in sociology.)
3. Esta é uma nova classe de medicamentos. (This is a new class of medication.)
4. A turma de ballet está muito animada hoje. (The ballet class/group is very excited today.)
5. O professor organizou a turma de alunos. (The teacher organized the class/group of students.)