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

No.

While the spelling, meaning, and grammar of "faz" are identical in both variants, there are differences in typical usage. In Brazil, "faz" is the standard and highly frequent way to express elapsed time (e.g., "faz dois anos"). In Portugal, while "faz" is understood, the verb "há" is much more common and natural for this purpose. Additionally, while "faz" is used for weather in both variants, Brazilians often use "faz" in contexts where a Portuguese person would more naturally prefer the verb "estar" (e.g., "faz calor" vs. "está calor").

Brazilian Portuguese Examples

1. Faz muito calor hoje em São Paulo. (It is very hot today in São Paulo.)
2. Faz dois anos que não viajo para a Europa. (It has been two years since I traveled to Europe.)
3. Ele faz o trabalho muito rápido. (He does the work very quickly.)
4. Essa comida faz bem à saúde. (This food is good for your health.)
5. Faz pouco tempo que ele chegou de viagem. (It hasn't been long since he arrived from his trip.)

Portuguese (Continental) Examples

1. Está muito calor hoje em Lisboa. (It is very hot today in Lisbon.)
2. Há dois anos que não viajo para a Europa. (It has been two years since I traveled to Europe.)
3. Ele faz o trabalho muito depressa. (He does the work very quickly.)
4. Essa comida faz bem à saúde. (This food is good for your health.)
5. Há pouco tempo que ele chegou de viagem. (It hasn't been long since he arrived from his trip.)