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

No.

While the core meaning of "to tidy" or "to organize" is shared, there are significant differences in typical usage and semantics. In Brazil, arrumar is commonly used to mean "to find" or "to obtain" (e.g., arrumar um emprego). In Portugal, this specific meaning is almost exclusively expressed by the verb arranjar. Additionally, for certain tasks like packing a suitcase, a Brazilian would use arrumar, whereas a Portuguese person would more naturally use fazer.

Brazilian Portuguese Examples:

1. Eu preciso arrumar meu quarto. (I need to tidy my room.)
2. Ela conseguiu arrumar um emprego novo. (She managed to get a new job.)
3. Estou arrumando a mala para as férias. (I am packing my suitcase for the holidays.)
4. Você pode arrumar essa bagunça? (Can you clean up this mess?)
5. Ele está arrumando o cabelo no espelho. (He is fixing his hair in the mirror.)

Continental Portuguese Examples:

1. Eu preciso de arrumar o meu quarto. (I need to tidy my room.)
2. Ela conseguiu arranjar um emprego novo. (She managed to get a new job.)
3. Estou a fazer a mala para as férias. (I am packing my suitcase for the holidays.)
4. Podes pôr esta confusão em ordem? (Can you put this mess in order?)
5. Ele está a arranjar o cabelo em frente ao espelho. (He is fixing his hair in front of the mirror.)