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

Yes.

The word "ioga" is identical in both Brazilian and Continental Portuguese in terms of meaning, spelling, and grammar. The only difference is in pronunciation. In Brazilian Portuguese, the vowels are generally pronounced more openly and clearly. In Continental Portuguese, vowels (especially unstressed ones) tend to be more "closed" or reduced, which can make the word sound more clipped or subtle to a Brazilian ear.

Brazilian Portuguese

1. Eu faço ioga todas as manhãs para relaxar. (I do yoga every morning to relax.)
2. A aula de ioga está lotada hoje. (The yoga class is crowded today.)
3. Você quer fazer uma aula de ioga comigo? (Do you want to do a yoga class with me?)
4. A ioga me ajuda a ter mais foco. (Yoga helps me have more focus.)
5. Ela comprou um tapete novo de ioga. (She bought a new yoga mat.)

Continental Portuguese

1. Pratico ioga todas as manhãs para relaxar. (I practice yoga every morning to relax.)
2. A aula de ioga está cheia hoje. (The yoga class is full today.)
3. Queres fazer uma aula de ioga comigo? (Do you want to do a yoga class with me?)
4. A ioga ajuda-me a ter mais foco. (Yoga helps me have more focus.)
5. Ela comprou um tapete de ioga novo. (She bought a new yoga mat.)