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

No.

The difference lies in typical usage and vocabulary. In Brazil, "ônibus" is the standard and universal term for a public bus. In Portugal, the word "ônibus" is not used for this purpose; instead, the standard term is "autocarro." Furthermore, the related vocabulary surrounding the word changes, such as the term for a "bus stop" and the verbs used to describe "catching" a bus.

Brazilian Portuguese

1. O ônibus passou muito rápido. (The bus passed by very fast.)
2. Eu perdi o ônibus para a escola. (I missed the bus to school.)
3. Tem um ponto de ônibus perto daqui. (There is a bus stop near here.)
4. O ônibus está lotado hoje. (The bus is crowded today.)
5. Vou pegar o ônibus às oito horas. (I will catch the bus at eight o'clock.)

European Portuguese

1. O autocarro passou muito rápido. (The bus passed by very fast.)
2. Eu perdi o autocarro para a escola. (I missed the bus to school.)
3. Há uma paragem de autocarro perto daqui. (There is a bus stop near here.)
4. O autocarro está cheio hoje. (The bus is full today.)
5. Vou apanhar o autocarro às oito horas. (I will catch the bus at eight o'clock.)