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

Yes

The word "cartas" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The difference is purely phonetic. In most Brazilian dialects, the final "s" is pronounced as a soft [s] (like the English "s" in "bus"), whereas in Continental Portuguese, the final "s" is pronounced as a [ʃ] (like the English "sh" in "ship").

Brazilian Portuguese Examples:

1. Eu gosto de jogar cartas com meu avô. (I like to play cards with my grandfather.)
2. Ele escreveu várias cartas de amor. (He wrote several love letters.)
3. As cartas do baralho estão espalhadas pela mesa. (The playing cards are scattered across the table.)
4. Ela recebeu as cartas de todos os amigos. (She received the letters from all the friends.)
5. Você viu as cartas que chegaram hoje? (Did you see the letters that arrived today?)

Continental Portuguese Examples:

1. Eu gosto de jogar cartas com o meu avô. (I like to play cards with my grandfather.)
2. Ele escreveu várias cartas de amor. (He wrote several love letters.)
3. As cartas do baralho estão espalhadas pela mesa. (The playing cards are scattered across the table.)
4. Ela recebeu as cartas de todos os amigos. (She received the letters from all the friends.)
5. Viste as cartas que chegaram hoje? (Did you see the letters that arrived today?)