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

Yes.

The word "amanhã" is identical in spelling, meaning, and grammatical function in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the vowels tend to be more "open" and the rhythm is more syllable-timed (each syllable has a similar length), resulting in a more melodic sound. In Continental Portuguese, the vowels (especially unstressed ones) are often more "closed" or reduced, and the rhythm is more stress-timed, which can make the word sound shorter or more clipped within a sentence.

Brazilian Portuguese Examples

1. A gente se vê amanhã. (We'll see each other tomorrow.)
2. Eu tenho que trabalhar amanhã cedo. (I have to work early tomorrow.)
3. Você vai viajar amanhã? (Are you going to travel tomorrow?)
4. Amanhã eu vou sair com meus amigos. (Tomorrow I am going to go out with my friends.)
5. Deixa pra amanhã. (Leave it for tomorrow.)

Continental Portuguese Examples

1. Vemo-nos amanhã. (We'll see each other tomorrow.)
2. Eu tenho de trabalhar amanhã cedo. (I have to work early tomorrow.)
3. Tu vais viajar amanhã? (Are you going to travel tomorrow?)
4. Amanhã vou sair com os meus amigos. (Tomorrow I am going to go out with my friends.)
5. Deixa isso para amanhã. (Leave that for tomorrow.)