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

No

While the spelling and the core meaning of "fórum" as a "place for discussion" are identical in both varieties, there is a significant difference in typical usage regarding the judicial system. In Brazil, "fórum" is the standard word used to refer to the physical courthouse building where legal proceedings take place. In Portugal, "fórum" is almost exclusively used to refer to discussion platforms (online or physical); when referring to the legal institution or the physical courthouse, a Portuguese person would naturally use the word "tribunal."

Brazilian Portuguese Examples

1. Eu preciso ir ao fórum hoje para entregar os documentos. (I need to go to the courthouse today to hand in the documents.)
2. O fórum da nossa cidade é muito antigo. (Our city's courthouse is very old.)
3. Postei uma dúvida no fórum de tecnologia. (I posted a question on the technology forum.)
4. O advogado está esperando no fórum. (The lawyer is waiting at the courthouse.)
5. Este fórum online é muito útil para aprender programação. (This online forum is very useful for learning programming.)

Portuguese (Portugal) Examples

1. Eu preciso de ir ao tribunal hoje para entregar os documentos. (I need to go to the court today to hand in the documents.)
2. O tribunal da nossa cidade é muito antigo. (Our city's court is very old.)
3. Postei uma dúvida no fórum de tecnologia. (I posted a question on the technology forum.)
4. O advogado está à espera no tribunal. (The lawyer is waiting at the court.)
5. Este fórum online é muito útil para aprender programação. (This online forum is very useful for learning programming.)