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

No

While the word refers to the same fish and shares the same spelling and grammatical properties, there is a difference in typical usage and pronunciation.

• Usage: In Portugal, "bacalhau" is frequently used metonymically to refer to the prepared dish itself (e.g., "I'll have a cod"). In Brazil, the word is primarily used to refer to the ingredient, and speakers are more likely to specify the dish or use "prato de" (plate of) to avoid implying they are eating a whole fish.
• Pronunciation: Brazilian Portuguese features more open, resonant vowels. European Portuguese uses much more closed, reduced vowels, which can make the unstressed syllables sound much more muffled or nearly silent to a Brazilian ear.

Brazilian Portuguese Examples

1. Eu gosto de comer bacalhau com batatas. (I like to eating cod with potatoes.)
2. O bacalhau está muito caro no mercado. (Cod is very expensive at the market.)
3. Você sabe como preparar bacalhau? (Do you know how to prepare cod?)
4. Eu comprei bacalhau para o jantar. (I bought cod for dinner.)
5. Este bacalhau está uma delícia. (This cod is delicious.)

European Portuguese Examples

1. Eu gosto de comer bacalhau com batatas. (I like to eating cod with potatoes.)
2. O bacalhau está muito caro no mercado. (Cod is very expensive at the market.)
3. Tu sabes preparar bacalhau? (Do you know how to prepare cod?)
4. Vou comer um bacalhau ao forno. (I am going to eat a cod [dish] baked in the oven.)
5. Estou a comer bacalhau. (I am eating cod.)