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

Yes.

The spelling, meaning, and grammatical function of "um" (as the masculine indefinite article or the number one) are identical in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the "m" serves as a nasalization marker for the vowel, often resulting in a more open and clearly nasalized [ũ] sound. In Continental Portuguese, the nasalization is much more subtle and "closed," and the "m" is often nearly silent, making the word sound like a very short, clipped "u" with a slight nasal quality.

Brazilian Portuguese Examples:

1. Eu vi um cachorro na rua. (I saw a dog in the street.)
2. Você tem um celular novo? (Do you have a new cell phone?)
3. Eu peguei um ônibus agora. (I caught a bus just now.)
4. Ele é um menino muito legal. (He is a very cool boy.)
5. Eu quero um suco de laranja. (I want an orange juice.)

Continental Portuguese Examples:

1. Eu vi um cão na rua. (I saw a dog in the street.)
2. Tu tens um telemóvel novo? (Do you have a new mobile phone?)
3. Eu apanhei um autocarro agora. (I caught a bus just now.)
4. Ele é um rapaz muito porreiro. (He is a very cool boy.)
5. Eu quero um sumo de laranja. (I want an orange juice.)