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

Yes

The word "tapete" has the same meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference is in pronunciation:

• In Brazilian Portuguese, the final "e" is pronounced as a clear /i/ sound (e.g., ta-pɛ-tʃi).
• In Continental Portuguese, the final "e" is reduced or "devoiced," sounding like a closed /ɨ/ or almost silent (e.g., ta-pɛt').

Brazilian Portuguese Examples

1. Eu comprei um tapete novo para a sala. (I bought a new rug for the living room.)
2. Por favor, limpe o tapete de entrada. (Please clean the entrance rug.)
3. O tapete está muito sujo de café. (The rug is very dirty with coffee.)
4. Coloque o tapete embaixo da mesa. (Put the rug under the table.)
5. Esse tapete é bem macio e confortável. (This rug is very soft and comfortable.)

Continental Portuguese Examples

1. Comprei um tapete novo para a sala. (I bought a new rug for the living room.)
2. Por favor, limpa o tapete da entrada. (Please clean the entrance rug.)
3. O tapete ficou manchado com o café. (The rug got stained with the coffee.)
4. Põe o tapete debaixo da mesa. (Put the rug under the table.)
5. Este tapete é muito macio. (This rug is very soft.)