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

No

While the word "fecho" shares the same core grammatical functions (as the first-person singular of the verb fechar and as a noun meaning "clasp/fastener"), there are significant differences in typical usage between the two dialects:

• Zipper: In Portugal, "fecho" is the standard term for the zipper slider (the part that moves). In Brazil, while "fecho" is understood, people more commonly use "zíper" to refer to the whole mechanism and "cursor" to refer specifically to the sliding part.
• Conclusion/End of an event: In Portugal, "fecho" is frequently used to denote the end or closing of an event (e.g., o fecho do festival). In Brazil, the word "encerramento" is the much more natural and standard choice for this context.

Brazilian Portuguese

1. Eu fecho a janela sempre que saio. (I close the window whenever I leave.)
2. O cursor do zíper quebrou. (The zipper slider broke.)
3. O encerramento do evento foi lindo. (The closing of the event was beautiful.)
4. Eu fecho a conta do banco agora. (I am closing the bank account now.)
5. O fecho da pulseira é muito pequeno. (The bracelet clasp is very small.)

European Portuguese

1. Eu fecho a janela sempre que saio. (I close the window whenever I leave.)
2. O fecho do casaco prendeu. (The zipper slider of the jacket got stuck.)
3. O fecho do evento foi lindo. (The closing of the event was beautiful.)
4. Eu fecho a conta do banco agora. (I am closing the bank account now.)
5. O fecho da pulseira é muito pequeno. (The bracelet clasp is very small.)