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

Yes

The meaning, spelling, and grammar of the word "rio" are identical in both Brazilian and Continental Portuguese. The difference is purely phonetic. In Brazilian Portuguese, the vowels are generally more open and clearly articulated. In Continental Portuguese, vowels are often more closed or even reduced, which can give the word a more "compressed" or muffled sound.

Brazilian Portuguese examples:

1. A gente vai nadar no rio hoje. (We are going to swim in the river today.)
2. O rio tá muito poluído. (The river is very polluted.)
3. Tem muito peixe nesse rio. (There are a lot of fish in this river.)
4. O nível do rio baixou bastante. (The river level has dropped a lot.)
5. Eu gosto de passar o dia no rio. (I like to spend the day at the river.)

Portuguese (Portugal) examples:

1. Vou nadar no rio hoje. (I am going to swim in the river today.)
2. O rio está muito poluído. (The river is very polluted.)
3. Há muitos peixes neste rio. (There are many fish in this river.)
4. O nível do rio desceu bastante. (The river level has dropped a lot.)
5. Gosto de passar o dia junto ao rio. (I like to spend the day by the river.)