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

No

While the dictionary definition of the verb relaxar is the same in both dialects, there is a significant difference in typical usage. In Brazilian Portuguese, "Relaxa" is a very common informal interjection and slang used to mean "Don't worry," "Take it easy," or "It's all good." It is a standard way to reassure someone. In Continental Portuguese, using "Relaxa" as a standalone phrase to reassure someone is much less common; a Portuguese person would more likely use "Não te preocupes" or "Calma" to convey that same sense of reassurance.

Brazilian Portuguese Usage

1. Relaxa, vai dar tudo certo. (Relax, everything will work out.)
2. Relaxa, eu resolvo isso agora. (Don't worry, I'll handle this now.)
3. Relaxa, cara, não foi nada demais. (Chill, man, it was no big deal.)
4. Relaxa, a gente se vê mais tarde. (Don't worry, we'll see each other later.)
5. Relaxa, eu não esqueci o seu presente. (Don't worry, I didn't forget your gift.)

Continental Portuguese Usage

1. Não te preocupes, vai correr tudo bem. (Don't worry, everything will go well.)
2. Não te preocupes, eu trato disso agora. (Don't worry, I'll take care of it now.)
3. Calma, não foi nada de especial. (Take it easy, it was nothing special.)
4. Não te preocupes, encontramo-nos mais tarde. (Don't worry, we'll meet later.)
5. Fica descansado, não me esqueci do teu presente. (Rest assured/Don't worry, I didn't forget your gift.)