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

Yes.

The word "pagar" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. Brazilian Portuguese is generally more "vocalic," with more open and clearly articulated vowels. In contrast, Continental Portuguese is more "consonantal," with a tendency to reduce or almost disappear unstressed vowels, resulting in a more clipped, rhythmic sound.

Brazilian Portuguese Examples

1. Eu vou pagar a conta agora. (I am going to pay the bill now.)
2. Você pode pagar no cartão de crédito? (Can you pay with a credit card?)
3. Ele esqueceu de pagar o boleto. (He forgot to pay the bank slip.)
4. Nós vamos pagar o almoço hoje. (We are going to pay for lunch today.)
5. Ela pagou o ingresso do cinema. (She paid for the movie ticket.)

Continental Portuguese Examples

1. Eu vou pagar a conta agora. (I am going to pay the bill now.)
2. Podes pagar com cartão? (Can you pay with card?)
3. Ele esqueceu-se de pagar a fatura. (He forgot to pay the invoice.)
4. Nós vamos pagar o almoço hoje. (We are going to pay for lunch today.)
5. Ela pagou o bilhete do cinema. (She paid for the movie ticket.)