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

Yes

The word "madrugada" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. It refers to the period between midnight and dawn. The only differences are in pronunciation:

• Consonants: In many Brazilian dialects (such as those in Rio de Janeiro or São Paulo), the "d" in "madrugada" is often palatalized, sounding like "dj." In Portugal, the "d" is strictly dental.
• Vowels and Rhythm: Brazilian Portuguese tends to have more open or varied vowel sounds and a more melodic, "syllable-timed" rhythm. Continental Portuguese uses more closed, unstressed vowels and a more "stress-timed" rhythm, which can make the word sound more clipped.

Brazilian Portuguese Examples

1. Eu trabalho de madrugada. (I work during the early morning hours.)
2. A festa acabou de madrugada. (The party ended in the early morning.)
3. Ele chegou de madrugada e nem avisou a galera. (He arrived in the early morning and didn't even let the group know.)
4. Dormir de madrugada é muito ruim para a saúde. (Sleeping in the early morning is very bad for your health.)
5. A gente saiu de madrugada para ver o sol. (We went out in the early morning to see the sun.)

European Portuguese Examples

1. Eu trabalho de madrugada. (I work during the early morning hours.)
2. A festa terminou de madrugada. (The party ended in the early morning.)
3. Ele chegou de madrugada e nem avisou a malta. (He arrived in the early morning and didn't even let the folks/group know.)
4. Dormir de madrugada é muito mau para a saúde. (Sleeping in the early morning is very bad for your health.)
5. Nós saímos de madrugada para ver o sol. (We went out in the early morning to see the sun.)