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

No.

While the spelling and core meaning (meaning "correct," "certain," or "true") are identical, there are differences in typical usage and pronunciation. In Brazil, "certo" is very frequently used as a conversational interjection to mean "Okay," "I see," or "Alright." In Portugal, while "certo" is used to denote something that is correct, a native speaker would more naturally use "Está bem" to express the same conversational "Okay." Additionally, the pronunciation differs significantly: Brazilian Portuguese tends to have more open, audible vowels, whereas Continental Portuguese relies heavily on vowel reduction, often making the unstressed "e" in "certo" almost silent.

Brazilian Portuguese Examples

1. "Você está certo." (You are right.)
2. "Certo, eu entendo." (Okay, I understand.)
3. "Isso é o certo a se fazer." (That is the right thing to do.)
4. "Tudo certo por aqui." (Everything is all right here.)
5. "Você vem amanhã, certo?" (You're coming tomorrow, right?)

Continental Portuguese Examples

1. "Tu tens razão." (You are right.)
2. "Está bem, eu percebo." (Alright, I understand.)
3. "Este é o modo correto." (This is the correct way.)
4. "Está tudo bem por aqui." (Everything is fine here.)
5. "Vens amanhã, não é?" (You're coming tomorrow, right?)