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

No.

While the spelling and core meaning of "aparecer" are identical in both variants, there are differences in grammar and typical usage. Specifically, when expressing an ongoing action (the continuous aspect), Brazilians typically use the gerund (aparecendo), whereas Portuguese people use the prepositional infinitive (a aparecer). Additionally, the way the verb is conjugated in the second person (imperative or informal address) differs because Brazilians primarily use você, while Portuguese people frequently use tu.

Brazilian Portuguese

1. Ele apareceu de surpresa na festa. (He showed up unexpectedly at the party.)
2. As manchas começaram a aparecer na pele. (The spots started to appear on the skin.)
3. Não apareça mais aqui! (Don't show up here anymore!)
4. O resultado vai aparecer amanhã. (The result is going to appear tomorrow.)
5. Ela está aparecendo cada vez mais no trabalho. (She is appearing/showing up more and more at work.)

Continental Portuguese

1. Ele apareceu de surpresa na festa. (He showed up unexpectedly at the party.)
2. As manchas começaram a aparecer na pele. (The spots started to appear on the skin.)
3. Não apareças mais aqui! (Don't show up here anymore!)
4. O resultado aparecerá amanhã. (The result will appear tomorrow.)
5. Ela está a aparecer cada vez mais no trabalho. (She is appearing/showing up more and more at work.)