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

Yes

The word "rua" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference lies in pronunciation, specifically the articulation of the initial "r." In most Brazilian dialects, the initial "r" is pronounced as an aspirated sound, similar to the English "h" in "house." In Continental Portuguese, the "r" is typically a more guttural, uvular, or velar sound.

Brazilian Portuguese examples:

1. Eu moro nesta rua. (I live on this street.)
2. A rua está muito cheia hoje. (The street is very crowded today.)
3. Eu vou para a rua agora. (I am going out/to the street now.)
4. Tem muito carro parado na rua. (There are many cars parked on the street.)
5. A rua é muito barulhenta. (The street is very noisy.)

Continental Portuguese examples:

1. Eu moro nesta rua. (I live on this street.)
2. A rua está muito cheia hoje. (The street is very crowded today.)
3. Eu vou à rua agora. (I am going out/to the street now.)
4. Há muitos carros estacionados na rua. (There are many cars parked on the street.)
5. A rua é muito barulhenta. (The street is very noisy.)