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

No

While the spelling and the core meaning (to wait or to hope) of "esperando" are identical in both variants, there is a significant difference in typical usage regarding the continuous aspect (actions happening right now).

• Brazilian Portuguese (BP): Uses the gerund (esperando) to express an ongoing action. For example: "Estou esperando" (I am waiting).
• Continental Portuguese (EP): Primarily uses the construction preposition a + infinitive (a esperar) or the expression à espera de to express the same ongoing action. While "estou esperando" is understood in Portugal, it sounds distinctly Brazilian.
• Vocabulary: When translating the context of "esperando," a Brazilian will use "ônibus," whereas a Portuguese person will use "autocarro."

Brazilian Portuguese Examples

1. Estou esperando o ônibus no ponto. (I am waiting for the bus at the stop.)
2. Ela está esperando você para o jantar. (She is waiting for you for dinner.)
3. Nós estamos esperando boas notícias. (We are waiting for/hoping for good news.)
4. O que você está esperando para começar? (What are you waiting for to start?)
5. Ele passou a tarde esperando o resultado. (He spent the afternoon waiting for the result.)

Continental Portuguese Examples

1. Estou à espera do autocarro na paragem. (I am waiting for the bus at the stop.)
2. Ela está à espera de ti para o jantar. (She is waiting for you for dinner.)
3. Estamos à espera de boas notícias. (We are waiting for/hoping for good news.)
4. O que é que estás à espera para começar? (What are you waiting for to start?)
5. Ele passou a tarde à espera do resultado. (He spent the afternoon waiting for the result.)