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

Yes

The spelling, meaning, and grammatical function of "montanha" are identical in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the vowels are generally more "open" and clearly articulated. In Continental Portuguese, vowels—especially unstressed ones—are often "reduced" or more closed, which can make the word sound more clipped or consonant-heavy to a Brazilian ear.

Brazilian Portuguese

1. "Essa montanha é muito alta." (That mountain is very high.)
2. "Eu amo subir montanhas no fim de semana." (I love climbing mountains on the weekend.)
3. "Tem muita neve no topo da montanha." (There is a lot of snow at the top of the mountain.)
4. "A vista da montanha é maravilhosa." (The view from the mountain is wonderful.)
5. "Eles fizeram uma trilha na montanha." (They made a trail on the mountain.)

Continental Portuguese

1. "Essa montanha é muito alta." (That mountain is very high.)
2. "Gosto de fazer caminhadas na montanha." (I like to go hiking in the mountains.)
3. "Há muita neve no topo da montanha." (There is a lot of snow at the top of the mountain.)
4. "A vista da montanha é magnífica." (The view from the mountain is magnificent.)
5. "Eles fizeram um trilho na montanha." (They made a trail on the mountain.)