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

Yes

The only differences between the word "rei" in Brazilian Portuguese and Continental Portuguese are in pronunciation. The spelling, meaning, and grammatical function of the word are identical in both dialects.

In Brazilian Portuguese, the "r" is typically an alveolar tap [ɾ] (similar to the "tt" in the English word "better") or a retroflex [ɻ] in certain regions. The "ei" diphthong is usually pronounced with a wide, open sound. In Continental Portuguese, the "r" is typically a uvular fricative [ʁ] (similar to the French "r"), and the vowels are often more closed or reduced.

Brazilian Portuguese Examples:

1. O Pelé é o rei do futebol. (Pelé is the king of football.)
2. Ele se acha o rei da festa. (He thinks he's the king of the party.)
3. O rei da Inglaterra visitou o Brasil. (The King of England visited Brazil.)
4. Ele é o rei do funk. (He is the king of funk.)
5. O rei de copas é a minha carta favorita. (The king of hearts is my favorite card.)

Continental Portuguese Examples:

1. O Pelé é o rei do futebol. (Pelé is the king of football.)
2. Ele acha-se o rei da festa. (He thinks he's the king of the party.)
3. O rei de Inglaterra visitou o Brasil. (The King of England visited Brazil.)
4. Ele é o rei do funk. (He is the king of funk.)
5. O rei de copas é a minha carta favorita. (The king of hearts is my favorite card.)