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

Yes

The word "cinema" is identical in spelling, meaning, and grammatical function in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowels are generally more open and the rhythm is more melodic. In Continental Portuguese, the unstressed vowels—specifically the "e" and the final "a"—are much more closed or reduced, which often makes the word sound shorter and more "clipped" to a Brazilian ear.

Brazilian Portuguese Examples

1. Eu adoro ir ao cinema nos finais de semana. (I love going to the cinema on weekends.)
2. O cinema do shopping está muito cheio hoje. (The mall's cinema is very crowded today.)
3. Você quer ir ao cinema ver aquele filme? (Do you want to go to the cinema to see that movie?)
4. Esse cinema tem poltronas muito confortáveis. (This cinema has very comfortable seats.)
5. O cinema é o meu lugar favorito para relaxar. (The cinema is my favorite place to relax.)

Continental Portuguese Examples

1. Adoro ir ao cinema ao fim de semana. (I love going to the cinema at the weekend.)
2. O cinema do centro comercial está lotado. (The shopping mall's cinema is crowded.)
3. Queres ir ao cinema ver um filme? (Do you want to go to the cinema to see a movie?)
4. Este cinema tem salas muito modernas. (This cinema has very modern theaters/rooms.)
5. O cinema é o meu lugar preferido para relaxar. (The cinema is my favorite place to relax.)