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

No.

While the spelling and the core definition of the condiment are identical, there is a difference in typical usage and pronunciation.

In Brazilian Portuguese, "maionese" is frequently used as a shorthand for salada de maionese (a specific type of potato salad dish). In Continental Portuguese, the word refers almost exclusively to the sauce itself; to refer to the dish, a Portuguese person would use the term salada de batata. Additionally, the pronunciation in Brazil is more open and vocalic (the final "e" is pronounced like an "i"), whereas in Portugal, the vowels are much more closed and subject to significant reduction.

Brazilian Portuguese

1. Eu adoro colocar maionese no meu sanduíche. (I love putting mayonnaise in my sandwich.)
2. A maionese do churrasco estava ótima. (The potato salad from the barbecue was great.)
3. Você pode pegar o pote de maionese na geladeira? (Can you grab the jar of mayonnaise from the fridge?)
4. Eu vou fazer uma maionese para o almoço. (I am going to make a potato salad for lunch.)
5. Essa maionese está muito temperada. (This mayonnaise [salad] is very well seasoned.)

Portuguese (Portugal)

1. Eu gosto de pôr maionese no meu sanduíche. (I like putting mayonnaise in my sandwich.)
2. A salada de batata do churrasco estava ótima. (The potato salad from the barbecue was great.)
3. Podes pegar o frasco de maionese no frigorífico? (Can you grab the jar of mayonnaise from the fridge?)
4. Eu vou fazer uma salada de batata para o almoço. (I am going to make a potato salad for lunch.)
5. Esta maionese está muito temperada. (This mayonnaise is very well seasoned.)