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

No.

While the core meaning of "pedido" (a request or a proposal) remains the same in both dialects, there is a significant difference in typical usage regarding commerce and food. In Brazil, "pedido" is the standard word used for both a request and a commercial or delivery order (e.g., an order placed on an app like iFood). In Portugal, "pedido" is used for a request, but for a commercial order or a package being delivered, the word "encomenda" is the natural choice. Furthermore, while a Brazilian might say "fazer um pedido" (to make an order) for food, a Portuguese person is more likely to use the verb "encomendar" (to order/to commission).

Brazilian Portuguese Examples

1. O meu pedido chegou. (My order arrived.)
2. Onde posso rastrear meu pedido? (Where can I track my order?)
3. Eu fiz um pedido de desculpas. (I made an apology.)
4. O garçom anotou o meu pedido. (The waiter wrote down my order.)
5. Vou fazer um pedido de pizza. (I'm going to order a pizza.)

Continental Portuguese Examples

1. A minha encomenda chegou. (My order arrived.)
2. Onde posso rastrear a minha encomenda? (Where can I track my order?)
3. Eu fiz um pedido de desculpas. (I made an apology.)
4. O empregado de mesa anotou o meu pedido. (The waiter wrote down my order.)
5. Vou encomendar uma pizza. (I'm going to order a pizza.)