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

Yes.

The word sonhar is identical in meaning, grammar, and spelling in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazil, the vowels are generally more open, and the "r" at the end of the word varies by region (often being more aspirated or retroflex). In Portugal, the vowels are more closed or reduced, and the "r" is typically a more distinct alveolar tap or trill.

Brazilian Portuguese Examples

1. Eu sonhei com você hoje. (I dreamed about you today.)
2. Ela sonota em viajar para o Japão. (She dreams of traveling to Japan.)
3. A gente sonha com o final de semana. (We dream about the weekend.)
4. Você já sonhou que estava voando? (Have you ever dreamed that you were flying?)
5. Ele sonha alto com a carreira dele. (He dreams big with his career.)

Continental Portuguese Examples

1. Eu sonhei contigo hoje. (I dreamed about you today.)
2. Ela sonha em viajar para o Japão. (She dreams of traveling to Japan.)
3. Nós sonhámos com o fim de semana. (We dreamed about the weekend.)
4. Tu já sonhaste que estavas a voar? (Have you ever dreamed that you were flying?)
5. Ele sonha grande com a carreira dele. (He dreams big with his career.)