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

No.

The difference lies in grammatical usage regarding the progressive aspect (actions happening right now). In Brazilian Portuguese, the gerund (tentando) is the standard way to express an ongoing action. In Continental Portuguese, the preposition a followed by the infinitive (a tentar) is the natural and standard way to express the same continuous action. While a Portuguese person would understand "tentando," they would rarely use it in everyday speech to describe a current process.

Brazilian Portuguese (Natural Usage)

1. Estou tentando terminar o trabalho. (I am trying to finish the work.)
2. Ele está tentando me ligar. (He is trying to call me.)
3. Nós estamos tentando entender o que aconteceu. (We are trying to understand what happened.)
4. Você está tentando me ajudar, né? (You are trying to help me, right?)
5. Eles estão tentando abrir a porta. (They are trying to open the door.)

Continental Portuguese (Natural Usage)

1. Estou a tentar terminar o trabalho. (I am trying to finish the work.)
2. Ele está a tentar telefonar-me. (He is trying to call me.)
3. Nós estamos a tentar perceber o que aconteceu. (We are trying to understand what happened.)
4. Estás a tentar ajudar-me, não estás? (Are you trying to help me, aren't you?)
5. Eles estão a tentar abrir a porta. (They are trying to open the door.)