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

No.

While the spelling and core definition are identical, there is a difference in typical usage. In Brazil, "telefone" is frequently used as a synonym for a phone number and can colloquially refer to a mobile phone. In Portugal, "telefone" refers almost exclusively to a landline (fixed-line) device, while "telemóvel" is the standard word for a mobile phone. There is also a difference in pronunciation: Brazilians typically reduce the final "e" to an "i" sound ([te-le-fo-ni]), whereas in Portugal, the "e" is a more closed, neutral vowel.

Brazilian Portuguese

1. Esqueci meu telefone em casa. (I forgot my phone at home.)
2. Você pode me passar seu telefone? (Can you give me your phone number?)
3. O telefone está tocando. (The phone is ringing.)
4. Eu vou atender o telefone. (I am going to answer the phone.)
5. Deixe seu telefone para contato. (Leave your phone number for contact.)

Continental Portuguese

1. Esqueci o meu telemóvel em casa. (I forgot my mobile phone at home.)
2. Podes dar-me o teu número? (Can you give me your number?)
3. O telefone está a tocar. (The phone is ringing.)
4. Vou atender o telefone. (I am going to answer the phone.)
5. Deixa o teu contacto. (Leave your contact [number].)