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

Yes

The word "dia" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In many Brazilian dialects (notably in Rio de Janeiro and São Paulo), the "d" is palatalized, meaning it is pronounced with a "j" sound, similar to the "j" in "jeep" (pronounced roughly as djee-ah). In Portugal, the "d" remains a dental or alveolar stop, sounding like the "d" in "dog" (pronounced as dee-ah).

Brazilian Portuguese

1. Bom dia! (Good morning!)
2. Todo dia eu vou para a academia. (Every day I go to the gym.)
3. O dia está muito bonito. (The day is very beautiful.)
4. Tenho muito trabalho hoje. (I have a lot of work today.)
5. Que dia chato! (What a boring day!)

Continental Portuguese

1. Bom dia! (Good morning!)
2. Todos os dias vou para o ginásio. (Every day I go to the gym.)
3. O dia está muito bonito. (The day is very beautiful.)
4. Tenho imenso trabalho hoje. (I have a lot of work today.)
5. Que dia aborrecido! (What a boring day!)