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

Yes

The spelling and fundamental meaning of "pão" are identical in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the nasal diphthong "ão" is typically more open and clearly articulated. In Continental Portuguese, the sound is often more closed, attenuated, or "swallowed" by the surrounding consonants.

Brazilian Portuguese examples:

1. Eu adoro comer pão na chapa no café da manhã. (I love eating toasted bread for breakfast.)
2. Você pode passar na padaria e comprar um pão? (Can you stop by the bakery and buy some bread?)
3. O pão francês acabou de sair do forno. (The French roll just came out of the oven.)
4. Tem muito pão na mesa. (There is a lot of bread on the table.)
5. Eu prefiro pão de forma para fazer sanduíches. (I prefer sliced bread to make sandwiches.)

Portuguese (Portugal) examples:

1. Gostaria de uma fatia de pão com manteiga. (I would like a slice of bread with butter.)
2. Vou comprar uma carcaça para o lanche. (I am going to buy a roll for my snack.)
3. Este pão de centeio é muito saboroso. (This rye bread is very tasty.)
4. Queres um pão com queijo? (Do you want a bread with cheese?)
5. O pão está muito fresco e fofinho. (The bread is very fresh and fluffy.)