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

Yes.

The meaning, spelling, and grammatical conjugation of "pedir" are identical in both Brazilian and Continental Portuguese. The differences are found in pronunciation and the syntactic structures used in surrounding sentences.

In Brazil, the final "r" is often aspirated (sounding like an "h") or retroflex (as in the American English "r"), and vowels are more open and distinct. In Portugal, the final "r" is much more subtle, and unstressed vowels are often "swallowed" or closed. Furthermore, while the word itself is the same, Brazilians naturally use the gerund (pedindo) to express ongoing actions, whereas the Portuguese naturally use the preposition "a" followed by the infinitive (a pedir).

Brazilian Portuguese Examples

1. Eu estou pedindo uma pizza. (I am ordering a pizza.)
2. Você pode me pedir um favor? (Can you ask me a favor?)
3. Ele pediu desculpas pelo erro. (He apologized for the error.)
4. A gente vai pedir um lanche. (We are going to order a snack.)
5. Ela pediu o telefone dele. (She asked for his phone number.)

Continental Portuguese Examples

1. Estou a pedir uma pizza. (I am ordering a pizza.)
2. Podes pedir-me um favor? (Can you ask me a favor?)
3. Ele pediu desculpa pelo erro. (He apologized for the error.)
4. Nós vamos pedir um lanche. (We are going to order a snack.)
5. Ela pediu o telefone dele. (She asked for his phone number.)