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

Yes

The spelling, meaning, and grammatical function of "manhã" are identical in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazil, the nasal vowel is generally pronounced with a more open and melodic resonance, whereas in Portugal, the realization of the nasalized vowel tends to be more closed and the rhythm of the word is more subtle.

Brazilian Portuguese Examples

1. Bom dia! Tenha uma ótima manhã. (Good morning! Have a great morning.)
2. Eu sempre estudo de manhã. (I always study in the morning.)
3. O café da manhã está pronto. (Breakfast is ready.)
4. Vamos nos encontrar amanhã de manhã. (Let's meet tomorrow morning.)
5. A manhã hoje está muito fresca. (The morning today is very fresh.)

Continental Portuguese Examples

1. Bom dia! Desejo-te uma excelente manhã. (Good morning! I wish you an excellent morning.)
2. Eu estudo sempre de manhã. (I study always in the morning.)
3. O pequeno-almoço está pronto. (Breakfast is ready.)
4. Vamos encontrar-nos amanhã de manhã. (Let's meet tomorrow morning.)
5. A manhã de hoje está muito fresca. (Today's morning is very fresh.)