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

Yes

The word "fase" has the same meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference lies in pronunciation:

• In Brazilian Portuguese, the final "e" is typically pronounced as a clear /i/ sound (sounding like fa-zee).
• In Continental Portuguese, the final "e" is unstressed and much more closed, often sounding like a very short, neutralized /ɨ/ or nearly silent (sounding like faz').

Brazilian Portuguese Examples

1. Estou passando por uma fase difícil na vida. (I am going through a difficult phase in life.)
2. A próxima fase do projeto começa na segunda-feira. (The next phase of the project starts on Monday.)
3. Olhe para a lua; ela está na fase cheia. (Look at the moon; it is in the full phase.)
4. Essa fase de crescimento é muito importante para o bebê. (This growth phase is very important for the baby.)
5. O time foi eliminado logo na primeira fase da competição. (The team was eliminated right in the first phase of the competition.)

Continental Portuguese Examples

1. Estou a passar por uma fase difícil na vida. (I am going through a difficult phase in life.)
2. A próxima fase do projeto começa na segunda-feira. (The next phase of the project starts on Monday.)
3. Olha para a lua; ela está na fase cheia. (Look at the moon; it is in the full phase.)
4. Esta fase de crescimento é muito importante para o bebé. (This growth phase is very important for the baby.)
5. A equipa foi eliminada logo na primeira fase da competição. (The team was eliminated right in the first phase of the competition.)