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

Yes.

The word "semana" is identical in meaning, spelling, and grammatical gender across both dialects. The primary difference lies in pronunciation. In Brazilian Portuguese, the vowels are generally more open and the rhythm is more syllable-timed. In Continental (European) Portuguese, the unstressed "e" undergoes significant vowel reduction, often sounding like a very short, nearly silent "i" or a schwa, giving the word a more clipped, stress-timed sound.

Brazilian Portuguese Examples

1. Eu vou viajar no final de semana. (I am going to travel on the weekend.)
2. Essa semana está sendo muito cansativa. (This week is being very tiring.)
3. A gente se vê na semana que vem. (We'll see each other next week.)
4. Tenho muita coisa para fazer essa semana. (I have a lot of things to do this week.)
5. Toda semana eu vou para a academia. (Every week I go to the gym.)

Portuguese (Continental) Examples

1. Vou viajar no fim de semana. (I am going to travel on the weekend.)
2. Esta semana está a ser muito cansativa. (This week is being very tiring.)
3. Vemo-nos na próxima semana. (We'll see each other next week.)
4. Tenho muito trabalho para entregar esta semana. (I have a lot of work to deliver this week.)
5. Todas as semanas vou ao ginásio. (Every week I go to the gym.)