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

No. While the meaning, spelling, and conjugation of "pôr" are identical in both dialects, there is a difference in typical usage. In Brazil, the verb colocar is much more frequent and is the preferred choice for the action of placing something in both formal and informal speech. In Portugal, pôr remains the standard, go-to verb for this action. Additionally, there is a difference in pronunciation: Brazilian Portuguese tends to have more open, clear vowels, while Continental Portuguese features significant vowel reduction (where unstressed vowels become shorter or nearly silent).

Brazilian Portuguese

1. Vou pôr o livro na mochila. (I'm going to put the book in the backpack.)
2. Põe o celular na mesa. (Put the cell phone on the table.)
3. Ele pôs a camiseta. (He put on the t-shirt.) Note: In Brazil, "camiseta" is the standard for a casual cotton shirt.
4. Ela pôs açúcar no café. (She put sugar in the coffee.)
5. Põe a mesa, por favor. (Set the table, please.)

Continental Portuguese

1. Vou pôr o livro na mochila. (I'm going to put the book in the backpack.)
2. Põe o telemóvel na mesa. (Put the mobile phone on the table.)
3. Ele pôs a t-shirt. (He put on the t-shirt.)
4. Ela pôs açúcar no café. (She put sugar in the coffee.)
5. Põe a mesa, por favor. (Set the table, please.)