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

Yes

The word "chega" is identical in spelling, grammar, and fundamental meaning in both Brazilian and Continental Portuguese. It functions as the third-person singular present indicative of the verb chegar (to arrive) and as an interjection meaning "enough" or "stop it." The only difference is pronunciation: in Brazil, the vowels are typically more open and the rhythm is more melodic, whereas in Portugal, the unstressed vowels are more reduced or closed, and the rhythm is more stress-timed.

Brazilian Portuguese

1. Ele chega muito tarde todos os dias. (He arrives very late every day.)
2. Chega de drama! (Enough with the drama!)
3. O ônibus chega agora no ponto. (The bus arrives at the stop now.)
4. Quando você chega de viagem? (When do you arrive from your trip?)
5. A água chega até o meu joelho. (The water reaches up to my knee.)

Continental Portuguese

1. Ele chega muito tarde todos os dias. (He arrives very late every day.)
2. Basta de drama! (Enough with the drama!)
3. O autocarro chega agora à paragem. (The bus arrives at the stop now.)
4. Quando é que tu chegas da viagem? (When do you arrive from your trip?)
5. A água chega ao meu joelho. (The water reaches up to my knee.)