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

Yes

The word "tarefa" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowels are generally more open and the rhythm is more syllable-timed, making the word sound clearer and more "musical." In Continental Portuguese, the unstressed vowels (especially the final "a") are much more closed, reduced, or even swallowed, resulting in a more stress-timed rhythm.

Brazilian Portuguese Usage

1. Tenho muita tarefa para fazer hoje. (I have a lot of tasks to do today.)
2. Essa tarefa de matemática é muito difícil. (This math assignment is very difficult.) 3. Dividimos a tarefa entre a equipe. (We divided the task among the team.)
3. Terminei minha tarefa de casa rapidinho. (I finished my homework very quickly.)
4. Essa tarefa é muito chata. (This task is very annoying.)

Continental Portuguese Usage

1. Tenho muito trabalho para fazer hoje. (I have a lot of work/tasks to do today.)
2. Este trabalho de matemática é muito difícil. (This math assignment is very difficult.)
3. Dividimos a tarefa entre a equipa. (We divided the task among the team.)
4. Terminei o meu trabalho de casa depressa. (I finished my homework quickly.)
5. Essa tarefa é muito aborrecida. (This task is very annoying.)