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

No

While the fundamental definition of the verb pegar remains the same, the typical usage differs significantly between the two variants. In Brazil, pegar is a "utility verb" used extensively for a wide range of actions, including catching transportation, catching an illness, or picking up an object. In Portugal, while pegar is used for physical grabbing, the verb apanhar is the much more natural and frequent choice for catching transport or contracting an illness. Furthermore, the vocabulary for the objects themselves often changes (e.g., celular in Brazil vs. telemóvel in Portugal).

Brazilian Portuguese Examples

1. Pegamos o ônibus agora. (We are taking the bus now.)
2. Pegamos um resfriado no parque. (We caught a cold at the park.)
3. Pegamos as chaves em cima da mesa. (We grabbed the keys on top of the table.)
4. Pegamos o celular para ver a hora. (We picked up the cell phone to check the time.)
5. Pegamos o atalho para evitar o trânsito. (We took the shortcut to avoid traffic.)

Continental Portuguese Examples

1. Apanhamos o autocarro agora. (We are taking the bus now.)
2. Apanhamos uma constipação no parque. (We catch a cold at the park.)
3. Apanhamos as chaves em cima da mesa. (We grab the keys on top of the table.)
4. Apanhamos o telemóvel para ver a hora. (We pick up the cell phone to check the time.)
5. Apanhamos o atalho para evitar o trânsito. (We take the shortcut to avoid traffic.)