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

No.

While the fundamental dictionary definitions of "passar" are identical in both variants, there are significant differences in typical usage, syntax, and idiomatic expressions. In Brazil, "passar" is frequently used in colloquial slang (e.g., "passar pano" to excuse someone's behavior), which is not used in the same way in Portugal. Furthermore, the grammatical construction surrounding the verb differs (the Brazilian use of the gerund "jogando" vs. the Portuguese construction "a jogar"), and Portuguese speakers often substitute "passar" with other verbs like "pôr" or "colocar" when referring to applying substances like cream.

Brazilian Portuguese Examples

1. Eu vou passar na sua casa mais tarde. (I'm going to stop by your house later.)
2. Ele passou o dia inteiro jogando videogame. (He spent the whole day playing video games.)
3. Preciso passar protetor solar antes de sair. (I need to apply sunscreen before going out.)
4. Não passa pano para ele, ele está errado! (Don't defend him, he's wrong!)
5. Eu estou passando muito calor hoje. (I am feeling very hot today.)

Continental Portuguese Examples

1. Vou passar por tua casa mais logo. (I'll stop by your house later.)
2. Ele passou o dia todo a jogar videojogos. (He spent the whole day playing video games.)
3. Tenho de pôr creme solar antes de sair. (I have to put on sunscreen before leaving.)
4. Não o defendas, ele está errado! (Don't defend him, he's wrong!)
5. Eu estou com muito calor hoje. (I am feeling very hot today.)