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

No

While the spelling, grammar, and literal meaning of "tchau" are identical in both dialects, there is a difference in typical usage. In Brazil, "tchau" is the standard, ubiquitous way to say goodbye across almost all social contexts, from casual to semi-formal. In Portugal, while "tchau" is used, it is often perceived as more informal or casual; Portuguese speakers more frequently rely on "adeus" for a standard farewell or "até [time]" (such as "até logo") to indicate they will see the person again soon.

Brazilian Portuguese Examples

1. Tchau, gente, até amanhã! (Bye, guys, see you tomorrow!)
2. Tchau, mãe, beijos! (Bye, mom, kisses!)
3. Tchau, a gente se vê depois. (Bye, we'll see each other later.)
4. Ele deu um tchauzinho e saiu. (He gave a little wave/bye and left.)
5. Tchau, até logo! (Bye, see you later!)

Portuguese (Portugal) Examples

1. Adeus, até amanhã! (Goodbye, see you tomorrow!)
2. Até logo, um abraço. (See you later, a hug.)
3. Até já, volto num instante. (See you in a bit, I'll be right back.)
4. Adeus, boa viagem! (Goodbye, have a good trip!)
5. Até breve, tudo de bom. (See you soon, all the best.)