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

No.

While the grammatical functions and spelling of "fala" are the same in both dialects, there is a significant difference in typical usage. In Brazil, "Fala!" is a very common informal greeting, serving as a shorthand for "What's up?" or "Tell me/Hey!". In Portugal, using "Fala!" as a standalone greeting is rare and would likely be interpreted only as a command to speak. There is also a difference in pronunciation: Brazilian Portuguese tends to pronounce vowels more openly and clearly, whereas European Portuguese features heavy vowel reduction, making the unstressed "a" at the end of the word much more subtle or nearly silent.

Brazilian Portuguese Examples

1. Fala, mano! Tudo beleza? (Hey, man! Is everything good?)
2. Ele fala muito rápido. (He speaks very fast.)
3. A fala dela é muito clara. (Her way of speaking is very clear.)
4. Fala logo o que você quer! (Just say what you want already!)
5. O que você fala não faz sentido. (What you say doesn't make sense.)

Portuguese (Portugal) Examples

1. Olá, pá! Tudo bem? (Hey, man! Everything well?)
2. Ele fala muito rápido. (He speaks very fast.)
3. O modo de falar dela é muito claro. (Her way of speaking is very clear.)
4. Diz logo o que tu queres! (Just say what you want already!)
5. O que tu dizes não faz sentido. (What you say doesn't make sense.)