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

No.

While the fundamental meaning of "relaxar" (to ease tension or unwind) is identical in both dialects, there is a difference in typical usage. In Brazil, the imperative form "Relaxa!" is a very common, native idiom used to mean "Don't worry" or "Take it easy." In Portugal, while "relaxar" is used to describe physical or mental relaxation, a person would much more likely use "Não te preocupes" to convey that same sentiment. Additionally, there are significant pronunciation differences: Brazilian Portuguese features more open vowels and a more aspirated "r" at the end of words, whereas Continental Portuguese features more closed, reduced vowels and a more clearly articulated "r."

Brazilian Portuguese Examples

1. Eu só quero relaxar no fim de semana. (I just want to relax on the weekend.)
2. Relaxa, cara, vai dar tudo certo. (Relax/Don't worry, man, everything will be fine.)
3. Depois do trabalho, eu gosto de relaxar ouvindo música. (After work, I like to relax listening to music.)
4. Você precisa relaxar um pouco mais. (You need to relax a little more.)
5. Vamos relaxar na praia hoje. (Let's relax at the beach today.)

Continental Portuguese Examples

1. Eu só quero descansar no fim de semana. (I just want to rest on the weekend.)
2. Não te preocupes, vai correr tudo bem. (Don't worry, everything will go well.)
3. Depois do trabalho, gosto de descontrair um pouco. (After work, I like to unwind a little.)
4. Precisas de relaxar um pouco mais. (You need to relax a little more.)
5. Vamos relaxar na praia hoje. (Let's relax at the beach today.)