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

Yes

The word "montanhas" is identical in spelling, meaning, and grammatical function in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowels are generally more open and the rhythm is more "musical" or syllable-timed. In Continental Portuguese, unstressed vowels are often reduced or "swallowed," making the word sound more closed and the rhythm more staccato or stress-timed.

Brazilian Portuguese Examples

1. Eu amo olhar para as montanhas. (I love looking at the mountains.)
2. Tem muitas montanhas em Minas Gerais. (There are many mountains in Minas Gerais.)
3. A gente foi fazer trilha nas montanhas. (We went hiking in the mountains.)
4. As montanhas estão muito lindas hoje. (The mountains are very beautiful today.)
5. É difícil escalar essas montanhas. (It is hard to climb those mountains.)

Portuguese (Portugal) Examples

1. Eu adoro observar as montanhas. (I love observing the mountains.)
2. Há muitas montanhas nesta região. (There are many mountains in this region.)
3. Fomos fazer uma caminhada nas montanhas. (We went for a hike in the mountains.)
4. As montanhas estão deslumbrantes hoje. (The mountains are stunning today.)
5. É difícil subir estas montanhas. (It is difficult to climb these mountains.)