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

No.

While the spelling and the core meaning of "fazem" (the third-person plural of the verb fazer) are identical, there is a difference in typical usage regarding the expression of elapsed time. In Brazil, it is very common in colloquial speech to use the plural "fazem" to denote time (e.g., "Fazem dois anos"), even though this is technically considered a grammatical error by prescriptive grammarians. In Portugal, this usage is strictly avoided; when referring to time, the verb must remain in the singular "faz," and "fazem" is reserved exclusively for instances where the subject is a plural noun or pronoun.

Brazilian Portuguese Examples:

1. Eles fazem o jantar toda noite. (They make dinner every night.)
2. Fazem dez anos que moro no Brasil. (It has been ten years since I moved to Brazil.)
3. As crianças fazem muita bagunça aqui. (The children make a lot of mess here.)
4. Eles fazem o trabalho bem rápido. (They do the work very fast.)
5. Fazem duas semanas que ele viajou. (It has been two weeks since he traveled.)

Portuguese (Portugal) Examples:

1. Eles fazem o jantar todas as noites. (They make dinner every night.)
2. Faz dez anos que moro no Brasil. (It has been ten years since I moved to Brazil.)
3. As crianças fazem muita confusão aqui. (The children make a lot of mess here.)
4. Eles fazem o trabalho muito depressa. (They do the work very quickly.)
5. Faz duas semanas que ele viajou. (It has been two weeks since he traveled.)