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

Yes

The word "pelo" is identical in both Brazilian and Continental Portuguese regarding its spelling, grammar, and semantic meaning. It functions either as the contraction of the preposition por + the masculine article o (meaning "by," "through," or "for the") or as a noun referring to "hair" or "fur." The only distinction is pronunciation: in Brazilian Portuguese, the unstressed "e" in "pelo" is typically pronounced with a more open and distinct vowel sound. In Continental Portuguese, unstressed vowels undergo significant reduction, meaning the "e" is often much more closed, neutralized, or almost silent.

Brazilian Portuguese Examples

1. O cachorro tem o pelo muito macio. (The dog has very soft fur.)
2. Eu enviei a mensagem pelo celular. (I sent the message via cell phone.)
3. Ele passou pelo maior desafio da vida. (He went through the greatest challenge of his life.)
4. Fizemos isso pelo bem de todos. (We did this for the good of everyone.)
5. Pelo menos ele chegou bem. (At least he arrived safely.)

Continental Portuguese Examples

1. O cão tem o pelo muito macio. (The dog has very soft fur.)
2. Eu enviei a mensagem pelo telemóvel. (I sent the message via mobile phone.)
3. Ele passou pelo maior desafio da vida. (He went through the greatest challenge of his life.)
4. Fizemos isso pelo bem de todos. (We did this for the good of everyone.)
5. Pelo menos ele chegou bem. (At least he arrived safely.)