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

No.

While the spelling and core meaning of "entender" remain the same, there is a difference in typical usage. In Brazil, "entender" is the standard, everyday verb used to express comprehension. In Portugal, although "entender" is used (often implying interpretation or intention), the verb "perceber" is much more frequent in daily conversation to mean "to understand" or "to get it." Furthermore, the pronunciation differs significantly: Brazilian Portuguese features more open, clear vowels, whereas Continental Portuguese involves more vowel reduction, making unstressed vowels sound much shorter or almost silent.

Brazilian Portuguese Examples:

1. Eu não entendi o que você disse. (I didn't understand what you said.)
2. Você consegue entender esse problema? (Can you understand this problem?)
3. Ele entendeu perfeitamente a explicação. (He understood the explanation perfectly.)
4. Eu entendo o seu lado. (I understand your side.)
5. Não entendi nada dessa aula. (I didn't understand anything from this class.)

Continental Portuguese Examples:

1. Eu não percebi o que disseste. (I didn't understand what you said.)
2. Tu consegues perceber este problema? (Can you understand this problem?)
3. Ele percebeu perfeitamente a explicação. (He understood the explanation perfectly.)
4. Eu percebo o teu lado. (I understand your side.)
5. Não percebi nada desta aula. (I didn't understand anything from this class.)