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

Yes

The word "janeiro" is identical in spelling, meaning, and grammatical gender in both Brazilian and Continental Portuguese. The only difference lies in pronunciation:

• Brazilian Portuguese: The vowels are typically more open and clearly articulated. The "e" in janeiro is pronounced as a clear /e/.
• Continental Portuguese: The vowels are more "closed" or reduced. The "e" in janeiro is often muffled or shortened, sounding much closer to a neutral, unstressed vowel (schwa).

Brazilian Portuguese Examples

1. Eu vou viajar em janeiro. (I am going to travel in January.)
2. Janeiro é um mês muito quente aqui no Brasil. (January is a very hot month here in Brazil.)
3. A gente tá organizando a viagem de janeiro. (We are organizing the January trip.)
4. Você tem algum plano para janeiro? (Do you have any plans for January?)
5. As férias de janeiro são demais! (The January holidays are awesome!)

Continental Portuguese Examples

1. Eu vou viajar em janeiro. (I am going to travel in January.)
2. Janeiro é um mês bastante frio em Portugal. (January is a quite cold month in Portugal.)
3. Estou a organizar a minha agenda para janeiro. (I am organizing my schedule for January.)
4. Tu tens algum plano para janeiro? (Do you have any plans for January?)
5. O frio de janeiro é muito intenso. (The January cold is very intense.)