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

Yes

The word "sim" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference is in pronunciation, specifically the phonetic realization of the nasal vowel [ĩ]. In Brazilian Portuguese, the nasalization tends to be more open and resonant, whereas in Continental Portuguese, the vowel may be pronounced with a slightly more closed or subtle resonance depending on the regional accent.

Brazilian Portuguese Examples

1. Sim, eu quero esse bolo. (Yes, I want this cake.)
2. Sim, você pode me ajudar. (Yes, you can help me.)
   3. Sim, eu já terminei a tarefa. (Yes, I have already finished the task.)
3. Sim, eu vou ao shopping. (Yes, I am going to the mall.)
4. Sim, eu te amo. (Yes, I love you.)

Continental Portuguese Examples

1. Sim, eu quero este bolo. (Yes, I want this cake.)
2. Sim, podes ajudar-me. (Yes, you can help me.)
3. Sim, eu já terminei a tarefa. (Yes, I have already finished the task.)
4. Sim, eu vou ao centro comercial. (Yes, I am going to the mall.)
5. Sim, eu amo-te. (Yes, I love you.)